Sunday

February 19, 2017
Number of results: 110,523

**Calculus**

Can you please help me get the solution to this limit without using squeeze theorem and l'hopitals rule lim x to 0 of x^3 sin(1/x) lim x to 0 of x^2 sin^2(1/x)

*January 11, 2017 by Liv*

**calculus**

using the squeeze theorem, find the limit as x->0 of x*e^[8sin(1/x)] what i did was: -1<=sin(1/x)<=1 -8<=8*sin(1/x)<=8 e^(-8)<=e^[8*sin(1/x)]<=e^(8) x*e^(-8)<=x*e^[8*sin(1/x)]<=x*e^(8) lim x->0 [x*e^(-8)] = 0 lim x->0 [x*e^(8)] = 0 hence, lim x...

*October 27, 2015 by Lid*

**maths**

find the limit of lim sin(x-1)/(x^2 + x - 2) x->1 without using l'hopitals rule

*October 28, 2010 by khela*

**calculus**

Lim sin2h sin3h / h^2 h-->0 how would you do this ?? i got 6 as the answer, just want to make sure it's right. and i couldn't get this one (use theorem 2) lim tanx/x x-->0 and also this one (use squeeze theorem to evaluate the limit) lim (x-1)sin Pi/x-1 x-->1

*September 6, 2010 by Jake*

**Calculus**

Following 2 questions are from a book at a point where L’Hopital’s Rule, Squeeze Theorem etc. have not been discussed and limits (A) and (B) as given below are to be evaluated by simple methods like algebraic simplification etc. 1. Int. of (xlogx)dx from 0 to 1. Indefinite...

*March 12, 2014 by MS*

**Calculus**

Following 2 questions are from a book at a point where L’Hopital’s Rule, Squeeze Theorem etc. have not been discussed and limits (A) and (B) as given below are to be evaluated by simple methods like algebraic simplification etc. 1. Int. of (xlogx)dx from 0 to 1. Indefinite...

*March 13, 2014 by MS*

**Calculus**

1.) Find the equation of the line that is tangent to the graph of y-y^3 at x=1. 2.) lim x->0 ((sin x*cos 2x)/3x) 3.) Show, using the squeeze theorem, that the limit of Xe^(sin 1/x) as x->0 is 0.

*January 25, 2015 by Amber*

**L'Hopitals Rule**

5) Use the L’Hopital’s method to evaluate the following limits. In each case, indicate what type of limit it is ( 0/0, ∞/∞, or 0∙∞) lim x→2 sin(x^2−4)/(x−2) = lim x→+∞ ln(x−3)/(x−5) = lim x→pi/4 (x&#...

*December 7, 2014 by Jane*

**calculus**

I am studying for a final exam and in our review packet we have this question, which I am having trouble with: lim (x-->0) ((e^x)+x)^(1/x) I tried this problem two ways. The first was with L'Hopitals rule... lim(x-->0) (1/x)((e^x)+x)^(1/x-1) * (e^x+1) but that doesn't ...

*May 20, 2009 by Jenna*

**calculus**

Suppose that f(x) is bounded: that is, there exists a constant M such that abs(f(x)) is < or equal to M for all x. Use the squeeze theorem to prove that lim x^2f(x)=0 as x approaches 0. if g(x) is Mx^2 then what is f(x) and h(x) according to the squeeze theorem. Also, what ...

*January 31, 2011 by Nayyab*

**calc**

need to find: lim as x -> 0 of 4(e^2x - 1) / (e^x -1) Try splitting the limit for the numerator and denominator lim lim x->0 4(e^2x-1) (4)x->0 (e^2x-1) ______________ = ________________ lim lim x->0 e^X-1 x->0 e^x-1 Next solve for lim x->0 and simplify

*September 26, 2006 by brian*

**Calculus**

Find the limit. Use L'Hopitals Rule if necessary. lim (x^2+3x+2)/(x^2+x) x -> 0

*November 12, 2007 by Britt*

**Calc Limits**

lim (1+x)^1/x. Give an exact answer. x->0 This reads: The limits as x approaches zero is (1 plus x) to the 1 divided by x. The log of each term is (1/x) ln (1 + x) = ln (1+x)/x Using L'Hopital's rule for the limit of f(x)/g(x), the limit if the log is lim f'/g' = lim [1/(1+...

*February 16, 2007 by Robert*

**Calculus**

L'Hospital's Rule Lim(lnx)^(x-1) x->1+ This is what I did so far... Form: 0^0 ln(lnx)/ (1/x-1) ----------------------------------- I am not sure if you could use L'Hospital Rule (as stated in the instruction)for the 2 problems below: lim [ln(y^2+2y)]/[lny]=1 y->0+ lim ...

*January 31, 2008 by Anonymous*

**math**

evaluate without using L'Hopital theorem the following limit lim x-->0 [(sin(x)-x)/(x-tan(x))] the answer is 0.5 but I want to know the steps to calculate such a problem

*January 29, 2017 by Al-Madhagi*

**math**

evaluate without using L'Hopital theorem the following limit lim x-->0 [(sin(x)-x)/(x-tan(x))] the answer is 0.5 but I want to know the steps to calculate such a problem

*January 29, 2017 by Al-Madhagi*

**calc bc (condensed**

is the limit as x approaches 0 of sin3x over 3x equal to zero? sorry-- basically this is my problem: lim [sin 3x / 4x) x-> 0 ~~~~I multiplied& eventually got to .75* lim (sin 3x / 3x) x-> 0 ~so i figured since (lim (sinx/x) x-> 0 was equal to zero, then lim (sin3x/ 3x...

*September 14, 2010 by APpreciative student*

**Calculus**

yes! tnk u ok? It's actually (x->0.) Find the limit of cot(x)-csc(x) as x approached 0? Lim [cot(x) - csc (x)] ..x->0 = Lim [(cos x -1)/sin x] ..x->0 Use L'Hopital's rule and take the ratio of the derivatives: Lim (-sin x/cos x) = 0 x->0 thank you very much...it ...

*May 6, 2007 by Maria*

**CALCULUS**

Could someone please solve these four problems with explanations? I'd like to understand how to get to the answers. Thank you! Without using a calculator: For each of the following, find: I. lim x->a- f(x) II. lim x->a+ f(x) III. lim x->a f(x) A. f(x)=|x^2+3x+2|/x^2-4...

*November 10, 2013 by Samantha*

**calc**

Use L’Hopital’s rule to find the limit of this sequence (n^100)/(e^n) ...If you do L'Hop. Rule it would take forever, right? You would always get an (e^n) at the bottom and will have to use the L'Hop. rule 100 times to find the limit...100*n^99, 9900n^98, and etc. Is there...

*February 1, 2012 by lola*

**Calculus**

Find the limit. lim 5-x/(x^2-25) x-->5 Here is the work I have so far: lim 5-x/(x^2-25) = lim 5-x/(x-5)(x+5) x-->5 x-->5 lim (1/x+5) = lim 1/10 x-->5 x-->5 I just wanted to double check with someone and see if the answer is supposed to be positive or negative. ...

*January 22, 2014 by S*

**Calculus. Limits. Check my answers, please! :)**

4. lim (tanx)= x->pi/3 -(sqrt3) 1 (sqrt3) ***-1 The limit does not exist. 5. lim |x|= x->-2 -2 ***2 0 -1 The limit does not exist. 6. lim [[x]]= x->9/2 (Remember that [[x]] represents the greatest integer function of x.) 4 5 ***4.5 -4 The limit does not exist. 7. lim...

*October 6, 2013 by Samantha*

**Calculus**

Use the graph to estimate the limit: lim x->0 sin(3x)/x When x is in degrees lim x->0 sin(3x)/x = ________ I thought the the answer was (3*180)/pi but it's not... please help... Thanks

*February 9, 2011 by Abi*

**calculus**

using L'Hospital's rule, evalutate; LIM as x->0 e^x +cos x / e^x + sin x I'm at LIM x->0 e^x+cosx / e^x +sinx but now I at a lost as to how to proceed.

*November 21, 2011 by redgy*

**CALCULUS - need help!**

Determine the limit of the trigonometric function (if it exists). 1. lim sin x / 5x (x -> 0) 2. lim tan^2x / x (x ->0) 3. lim cos x tan x / x (x -> 0)

*October 1, 2007 by ac*

**calculus **

find the limit without using L'Hopital's Rule Lim(X->-4) (16-x^2 / x+4)

*January 25, 2017 by jaime*

**calculus again**

Suppose lim x->0 {g(x)-g(0)} / x = 1. It follows necesarily that a. g is not defined at x=0 b. the limit of g(x) as x approaches equals 1 c.g is not continuous at x=0 d.g'(0) = 1 The answer is d, can someone please explain how? Thanks. lim x->0 {g(x)-g(0)} / x = 1. You ...

*December 3, 2006 by Jen*

**pre calc help please!!!!**

given that lim f(x) = 5 x->x and lim g(x) = -7 x -> c find lim [f(x)+g(x)]^2 x-> c a. limit does not exist b. -175 c. 4 d. 245 e. -70

*September 2, 2016 by lottie*

**Calculus**

Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x>0... Should i use the formula e= lim as x->0 (1+x)^(1/x) or e= lim as x->infinity (1+1/n)^n Am i able to substitute in x/n for x? and then say that e lim x ->0 (1+x/n)^(1/(x/n)) and then raise it ...

*November 8, 2011 by Frederick E.*

**Calculus**

Below are the 5 problems which I had trouble in. I can't seem to get the answer in the back of the book. Thanks for the help! lim (theta-pi/2)sec(theta) theta->pi/2 Answer: -1 I am not sure what to do here. lim (tan(theta))^(theta) theta->0+ Answer:1 ln(tan(theta))/(1/...

*February 17, 2008 by Anonymous*

**Calculus**

Using l'hopitals rule, evaluate the following: Lim x-->infinity Inx/2(x)^1/2 Limx-->0 (1/x - 1/e^x -1) I tried both multiple times and I'm still not getting an answer. For the first one I tried l'hopitals rule 3 times and I'm still getting infinity over infinity for an ...

*May 10, 2016 by Maya*

**calculus**

(lim x --> +inf) of (x^2 - [[x^2]])/2 using Squeeze theorem only thank you so much in advance! its for my midterm tonight!

*October 23, 2009 by cameron*

**survey of clac**

g(x)={x+6, for x<-2, -1/2x+1, for x> or equal to -2, find the limit: lim g(x)= lim g(x)= x-->-2^- x-->-2^+ lim g(x)= lim g(x)= x-->-2^+ x-->4^-

*September 24, 2010 by samir*

**Calculus**

Find the positive integers k for which lim ->0 sin(sin(x))/x^k exists, and then find the value the limit. (hint:consider first k=0, then k=1. Find the limit in these simple cases. Next take k=2 and finally consder k>2 and find the limit in these cases as well) I did this...

*September 24, 2011 by Sybil Jones*

**Calculus**

Find the indicated limits. If the limit does not exist, so state, or use the symbol + ∞ or - ∞. f(x) = { 2 - x if x ≤ 3 { -1 + 3x - x^2 if x > 3 a) lim 3+ f(x) x->3 b) lim 3- f(x) x->3 c) lim f(x) x->3 d) lim ∞ f(x) x->3 e) lim -∞ f...

*October 8, 2011 by Blue*

**Calculus**

Find the indicated limits. If the limit does not exist, so state, or use the symbol + ∞ or - ∞. f(x) = { 2 - x if x ≤ 3 { -1 + 3x - x^2 if x > 3 a) lim 3+ f(x) x->3 b) lim 3- f(x) x->3 c) lim f(x) x->3 d) lim ∞ f(x) x->3 e) lim -∞ f...

*October 9, 2011 by Chris*

**limit calc question**

2 questions!!! 1. Limit X approaching A (X^1/3-a^1/3)/ x-a 2. LiMIT x approaching 0 (1/3+x – 1/3) /x On the first, would it help to write the denominator (x-a) as the difference of two cubes ((x^1/3 cubed - a^1/3 cubed) second. use LHopitals rule. Take the derivative of the ...

*March 2, 2007 by kev*

**calculus-limits??**

i keep on doing something wrong on this problem,i guess im forgetting to add or subtract some number. use f'(x)=lim h-->0 f(x+h)-f(x)/h to find the limit: lim h-->0 sin^(3)4(x+h)-sin^(3)4x/h

*March 24, 2010 by JJ*

**Calculus**

Find the following limits algebraically or explain why they don’t exist. lim x->0 sin5x/2x lim x->0 1-cosx/x lim x->7 |x-7|/x-7 lim x->7 (/x+2)-3/x-7 lim h->0 (2+h)^3-8/h lim t->0 1/t - 1/t^2+t

*March 15, 2012 by angie*

**Calculus**

Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x>0... Should i use the formula e= lim as x->0 (1+x)^(1/x) or e= lim as x->infinity (1+1/n)^n Am i able to substitute in x/n for x? and then say that e lim x ->0 (1+x/n)^(1/(x/n)) and then raise it ...

*November 9, 2011 by Frederick E.*

**Calc Please Help**

Are these correct? lim x->0 (x)/(sqrt(x^2+4) - 2) I get 4/0= +/- infinity so lim x->0+ = + infinity? and lim x->0- = + infinity? lim x->1 (x^2 - 5x + 6)/(x^2 - 3x + 2) I get 2/0, so lim x-> 1+ = - infinity? and lim x->1- = + infinity? lim h->0 [(-7)/(2+h^2...

*October 14, 2010 by Chelsea*

**Calculus L'Hopital Rule**

lim x->0 (x)sin(x)/1-cos(x). They both go to 0 so 0/0. now take L'H and product rule of top? lim x->0 (1)sin(x)+ cos(x)(x)/1-cos(x) what next? how do i solve from here?

*October 18, 2012 by Greg*

**Calc 1**

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→0 (sin^−1 x)/7x Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→0 x/(tan...

*April 20, 2015 by TayB*

**Calc. Limits**

Are these correct? lim x->0 (x)/(sqrt(x^2+4) - 2) I get 4/0= +/- infinity so lim x->0+ = + infinity? and lim x->0- = + infinity? lim x->1 (x^2 - 5x + 6)/(x^2 - 3x + 2) I get 2/0, so lim x-> 1+ = - infinity? and lim x->1- = + infinity? lim h->0 [(-7)/(2+h^2...

*October 13, 2010 by Chelsea*

**calc**

Are these correct? lim x->0 (x)/(sqrt(x^2+4) - 2) I get 4/0= +/- infinity so lim x->0+ = + infinity? and lim x->0- = + infinity? lim x->1 (x^2 - 5x + 6)/(x^2 - 3x + 2) I get 2/0, so lim x-> 1+ = - infinity? and lim x->1- = + infinity? lim h->0 [(-7)/(2+h^2...

*October 13, 2010 by Chelsea*

**Math- Calculus**

I need help with these problems, I cannot find a similar example to help me in the book: 1. Find lim x->infinity (e^(-2x) + sin x). 2. Find the derivative of sqrt(9-x) using the limit process. 3. Find lim x-> -infinity (x + sqrt(x^2 + 2x)). 4. Show that the equation e^x...

*February 9, 2015 by Amber*

**calculus help**

consider lim -->0^+ 1)sin(4x)/sin(3x) find the limit using a table of values 2)based on your answer what should the limit equal?

*September 12, 2012 by Kimberly*

**Pre-Calculus**

Which of the following shows the correct notation for “The limit of x^2 - 1 as x approaches 3. A. lim x^2-1 x->3 B. lim3 x->x^2-1 C. lim(x^2-3) x->x^2-1 D. lim(x^2-1) x->3 Thank you

*December 12, 2016 by Iris*

**Pre-Cal**

Given that lim x-> f(x)=6 and that lim x-> g(x)= -4, evaluate the following limit. Assume that c is a constant. lim -2f(x) - 12 / g(x). x->. I did -2(6) - (12/-4) -12 - (-3) -12 + 3 -9

*May 5, 2010 by Randy*

**pre-cal**

Given that lim x->c f(x)=6 and that lim x->c g(x)= -4, evaluate the following limit. Assume that c is a constant. The x in front of the f is confusing me. lim [xf(x) + 3 g(x)]^2 x->c

*May 8, 2010 by Randy*

**college math**

Use a table to frind the indicated limit. 3 7. lim(4x ) x-2 2 8. lim (2x + 1) x-3 x + 1 9. lim 2 x-0 x + 1

*October 19, 2011 by Rick*

**CALCULUS LIMITS**

What is the following limit? lim as n goes to infinity of (pi/n) (sin(pi/n) + sin(2pi/n) + sin(3pi/n) +...+ sin(npi/n)) = I.) lim as n goes to infinity sigma (n and k=1) of pi/n sin(kpi/n) II.) Definite integral from 0 to pi of sin(x)dx III.) 2 A.) I only B.) II only C.) III ...

*May 31, 2012 by ANONYMOUS*

**Calculus**

What is the following limit? lim as n goes to infinity of (pi/n) (sin(pi/n) + sin(2pi/n) + sin(3pi/n) +...+ sin(npi/n)) = I.) lim as n goes to infinity sigma (n and k=1) of pi/n sin(kpi/n) II.) Definite integral from 0 to pi of sin(x)dx III.) 2 A.) I only B.) II only C.) III ...

*May 31, 2012 by Anonymous (Please Help)*

**Calculus-Limits**

Okay, i posted this question yesterday, however, I did not really understand the answer I received. If your the one who answered my question, could you please elaborate. If not, could you try to answer this tough, for me, question. Thanks a lot. lim x-->0 Square root (1 + ...

*March 6, 2007 by Matt*

**maths**

find the limit as x approaches 0 of the function: (e^x.sinx)/x without using hopitals rule

*November 26, 2009 by eddie*

**Limits**

Let lim f(x) =16 as x->4 and lim g(x) =8 as x->4 Use the limit rules to find lim [cos(pi*f(x)/g(x))] as x->4

*February 20, 2014 by Andy*

**calculus**

The limit as x approaches infinity of (e^x+x)^(1/x). I got that it diverges, but I'm not sure if I made a mistake. My work: lim(e+x^(1/x)) lim(e+(1/x^x)) lim(ex^x+1)/x^x l'hopital:lim(e^(e(lnx+1))+1)/e^(lnx+1) diverges?

*September 1, 2010 by Dave*

**Check my CALCULUS work, please! :)**

Question 1. lim h->0(sqrt 49+h-7)/h = 14 1/14*** 0 7 -1/7 Question 2. lim x->infinity(12+x-3x^2)/(x^2-4)= -3*** -2 0 2 3 Question 3. lim x->infinity (5x^3+x^7)/(e^x)= infinity*** 0 -1 3 Question 4. Given that: x 6.8 6.9 6.99 7.01 7.1 7.2 g(x) 9.44 10.21 10.92 -11.08 -...

*November 11, 2013 by Samantha*

**MATH - Calculus (2)**

if lim f(x) = a^3 x->a and if lim g(x) = a^2 x->a calculate the following limit: lim f(x)*(x-a)/(x^3-a^3)*g(x) = x->a

*September 11, 2011 by Raf*

**Calculus**

Evaluate each limit. If it exists. a) Lim x^3 + 1 x->1 ------- x + 1 b) Lim 3x^2 - x^3 x->0 ---------- x^3 + 4x^2 c) Lim 16 - x x->16 --------- (√x) - 4

*June 21, 2012 by Jessica*

**calculus**

calculate the lim as x-> pi (cos(x)+1)/(x-pi) using the special limit lim x->0 sinx/x

*November 13, 2009 by jeff*

**Calculus**

Use L'Hoplital's rule to find the limit. Lim x->0 (3-3cos(x))/(sin(4x))

*August 10, 2016 by Sam*

**calculus**

Find lim (with x¨‡ under it) (x^2-1)/x or state that the limit does not exist. I'm so lost with what to do with limits...I tried to simplify the expression to lim x+lim -1/x, but from there I'm pretty dumbfounded. If anybody could help me out I'd really appreciate it.

*May 23, 2008 by Lisa*

**Calculus**

I have two similar problems that I need help completing. Please show all your work. Question: Find the limit L. Then use the å-ä definition to prove the limit is L. 1. lim (2x+5) x->3 2. lim 3 x->6 Thank you for your anticipated help!!

*June 27, 2012 by Liz*

**calculus**

1. integral -oo, oo [(2x)/(x^2+1)^2] dx 2. integral 0, pi/2 cot(theta) d(theta) (a) state why the integral is improper or involves improper integral (b) determine whether the integral converges or diverges converges? (c) evaluate the integral if it converges CONFUSE: how would...

*February 10, 2008 by Anonymous*

**Calc-Math**

Evaluate the limit using l'hospitals rule. lim->0 (3^x-6^x)/x. Do not know where to even begin on this one... please help.

*June 2, 2016 by Lisa*

**Pre-cal**

Please determine the following limits if they exist. If the limit does not exist put DNE. lim 2+6x-3x^2 / (2x+1)^2 x-> - infinity lim 4n-3 / 3n^2+2 n-> infinity I did lim 2+6x-3x^2 / (2x+1)^2 x-> - infinity (2+6x-3x²)/(4x²+4x+1) (2/x² + 6/x -3)/(4 + 4/x + 1/x²) as...

*May 9, 2010 by Randy*

**Calc 1**

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→0 (7x−sin 7x)/(7x−tan 7x)

*April 20, 2015 by TayB*

**Math**

Find the limit if it exists. lim 1/(x-2) = infinity x→2+ lim 1/(x-2) = negative infinity x→2- lim 1/(x-2) = Does not exist x→2 lim (3x+2) = infinity x→∞ lim 999/(x^3) = 0 x→-∞ Can someone check to make sure that I am correct?

*May 19, 2016 by David*

**Calculus..more help!**

I have a question relating to limits that I solved lim(x-->0) (1-cosx)/2x^2 I multiplied the numerator and denominator by (1+cosx) to get lim(x->0) (1-cos^2x)/2x^2(1+cosx) = lim(x->0)sin^2x/2x^2(1+cosx) the lim(x->0) (sinx/x)^2 would =1 I then substituted the ...

*February 21, 2009 by Alex*

**math**

i need some serious help with limits in pre-calc. here are a few questions that i really do not understand. 1. Evaluate: lim (3x^3-2x^2+5) x--> -1 2. Evaluate: lim [ln(4x+1) x-->2 3. Evaluate: lim[cos(pi x/3)] x-->2 4. Evaluate: lim x^2+x-6/x^2-9 x--> -3 5. ...

*July 13, 2010 by Dani*

**calculus**

Find the lim x->infinite (x/[3x+5]) where [] denotes the greatest integer function use the squeeze theorem.

*October 5, 2009 by jeff*

**CALCULUS**

What is the following limit? lim as n goes to infinity of (pi/n) (sin(pi/n) + sin(2pi/n) + sin(3pi/n) +...+ sin(npi/n)) = I.) lim as n goes to infinity sigma (n and k=1) of pi/n sin(kpi/n) II.) Definite integral from 0 to pi of sin(x)dx III.) 2 A.) I only B.) II only C.) III ...

*May 31, 2012 by ANONYMOUS*

**Calculus Help Please Urgent!!!**

find the limit algebraically. Use L'Hospital's Rule where appropriate. If there is a moare elementary method, consider using it. If L'Hospital's Rule doesn't apply, explain why lim -> 0 (cot(x)-(1/x)) show work please!!!

*April 13, 2014 by Selda*

**Calculus (lim)**

consider the statement lim x³-6x²+11x-6 / x-1 = 2 x->1 Using the definition of the limit, state what must be true for the above limit to hold, that is, for every ..., there is ..., so that.... Use a specific function and limit not just f and L. Verify the limit is true ...

*May 7, 2014 by Tommy feels dumb*

**Math**

Find the limit f(x) = -(x^2)/(x+3) a) lim f(x) x-3^- b) lim f(x) x-3^+ c) lim f(x) x-3 I know that a is dne because of the graph and that b is -infinity. And that c is dne because they are not the same. But I do not know how to do this algebraically. Thank you

*January 9, 2017 by John*

**calculus**

lim (x^3-1)/(x^3+2x^2y+xy^2-x^2-2xy-y^2) (x,y)->(1,0) my question is can you approach (1,0) with y=x and does that change the the limit to lim f(x,x) (x,x)->(1,1) in which case i get 3/4 as the limit. and if this is not how i go about doing it can you point me in the ...

*February 28, 2012 by Bryant*

**Calc 1**

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→∞ x^7e^−x^6 Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→∞...

*April 20, 2015 by TayB*

**CALCULUS**

Evaluate each of the following. (a) lim x->0(e^x)-1-x/ x^2 (b) lim x->0 x-sinx/x^3 (c) lim x->infinity (In x)^2/x (d) lim x->0+ (sinx)In x (e) lim x->0+ (cos3x)^5/x (f) lim x->1+ ((1/x-1) -(1/In x))

*December 5, 2007 by Anonymous*

**Calculus, please check my answers!**

1. Evaluate: lim x->infinity(x^4-7x+9)/(4+5x+x^3) 0 1/4 1 4 ***The limit does not exist. 2. Evaluate: lim x->infinity (2^x+x^3)/(x^2+3^x) 0 1 3/2 ***2/3 The limit does not exist. 3. lim x->0 (x^3-7x+9)/(4^x+x^3) 0 1/4 1 ***9 The limit does not exist. 4.For the ...

*October 7, 2013 by Samantha*

**Calculus - ratio test**

infinity of the summation n=1: (e^n)/(n!) [using the ratio test] my work so far: = lim (n->infinity) | [(e^n+1)/((n+1)!)] / [(e^n)/(n!)] | = lim (n->infinity) | [(e^n+1)/((n+1)!)] * [(n!)/(e^n)] | = lim (n->infinity) | ((e^n)(e^1)(n!)) / ((n+1)(n!)(e^n)) | ..the e^n...

*July 29, 2007 by COFFEE*

**math**

I have to evaluate the limit of these problems and I can't figure them out! 1.) Lim x-> 1 x^2+x-2/x^2-x 2.) (please note that the -2 is not under the square root) Lim x->0 sqroot 4+h -2/ h

*June 18, 2012 by please help!*

**Calc**

I have a test soon.. and I really need to know how to do this problem.. please help!!! lim as x-->0 sin^2(x)/tan(x^2) the answer is 1, but I have no clue how to get that! Use series expansions. Look up Taylor expansion on google and study that topic first. Using series ...

*March 30, 2007 by Urgent*

**Math(calculus)**

Evaluat d 4lowing1.lim x/|x| x-->0 2.lim x->1 sqrt(x^2+2- sqrt3)/x-1 3.lim n->~ f(n)=(1+1/n)^sqrtn 4. limx->0 f(x)= (12^x-3^x-4^x+1)/xtanx 5. Lim x->3 (x^n-3^n)^n/(n-3)^n

*February 5, 2012 by Bash*

**calculus1**

Find limit if exists 1. Lim x goes to 0 x^2cos(1/x^3) 2.lim x goes to 1 to the left 4x/x^2+2x-3 3. Lim x goes to π to the right cscx

*June 10, 2015 by Yumin*

**calculus**

f(x)= 3x+2, x<0 3, x=0 x^2+1, x>0 g(x)= -x+3, x<1 0, x=1 x^2, x>1 find a) lim x->0+ g(f(x)) b)lim x->0- g(f(x)) c) lim x->1+ f(g(x)) d)lim x->1- f(g(x)) I am trying to understand these. Help appreciated. Have a test soon.

*December 17, 2010 by Jim*

**Math**

Find the limit if it exists. lim 1/(x-2) x→2+ lim 1/(x-2) x→2- lim 1/(x-2) x→2 lim (3x+2) x→∞ lim 999/(x^3) x→-∞

*May 19, 2016 by David*

**Math**

Find the limit if it exists. lim 1/(x-2) x→2+ lim 1/(x-2) x→2- lim 1/(x-2) x→2 lim (3x+2) x→∞ lim 999/(x^3) x→-∞

*May 19, 2016 by David*

**Calculus help, please!**

1. Evaluate: lim x->infinity(x^4-7x+9)/(4+5x+x^3) 0 1/4 1 4 The limit does not exist. 2. Evaluate: lim x->infinity (2^x+x^3)/(x^2+3^x) 0 1 3/2 2/3 The limit does not exist. 3. lim x->0 (x^3-7x+9)/(4^x+x^3) 0 1/4 1 9 The limit does not exist. 4.For the function g(f)=4f...

*October 6, 2013 by Samantha*

**Calculus**

Evaluate the limit using L'Hospital's rule if necessary. lim as x goes to +infinity x^(6/x)

*February 19, 2010 by <3*

**Calculus**

Using L'Hopital's Rule, find the limit: lim x->0+ (as x approaches 0 from the right) of sinx/x^(1/3)

*March 28, 2011 by Justin*

**calculus - ratio test**

infinity of the summation n=1: (e^n)/(n!) [using the ratio test] my work so far: = lim (n->infinity) | [(e^n+1)/((n+1)!)] / [(e^n)/(n!)] | = lim (n->infinity) | [(e^n+1)/((n+1)!)] * [(n!)/(e^n)] | = lim (n->infinity) | ((e^n)(e^1)(n!)) / ((n+1)(n!)(e^n)) | ..the e^n...

*July 30, 2007 by COFFEE*

**Math**

Evaluate: (without using Hopital's rule) d) lim (6-3x)/(((5x+6)^1/2)-4) x->2

*September 27, 2011 by Raf*

**calculus**

Using the 4 step method fidn the derivative of F(x) =1/(x^2) 1) I got /(x^2+2xh+h^2) 2)2xh+h^2/(x^2+2xh+h^2)(x^2) 3)2x+h/(x^2+2xh+h^2)(x^2) 4)1/x I don't understand why I got this problem wrong on my test can you explain the correct way? The second step is wrong, it should be ...

*October 2, 2006 by Tom*

**Calculus**

Let f be a function defined for all real numbers. Which of the following statements must be true about f? Which might be true? Which must be false? Justify your answers. (a) lim of f(x) as x approaches a = f(a) (b) If the lim of f(x)/x as x approaches 0 = 2, then f(0)=0. (c) ...

*August 28, 2015 by Anonymous*

**calculus**

It is known that x 2 + 4x ≤ f(x) ≤ -x 2 -4x the interval [-4, 0]. Use the Squeeze Theorem to evaluate the limit as x approaches negative 2 of f of x. -4 0 4 Squeeze Theorem does not apply

*February 5, 2014 by ashley*

**Calculus**

Use pinching theorem to evaluate lim x-->1 ((x-1)sin(1/x-1)) I'm confused in the pinch theorem analytically

*June 9, 2016 by Anonymous*

**Math - Calculus**

f(x) = { x^2sin(1/x), if x =/= 0 0, if x=0} a. find lim(x->0)f(x) and show that f(x) is continuous at x=0. b, find f'(0) using the definition of the derivative at x=0: f'(x)=lim(x->0) (f(x)-f(0)/x) c. Show that lim(x->0)f'(x) does not exist. In particular, this means ...

*February 16, 2017 by Anonymous*

**Pre Cal help please!!**

given f(x) = { 2x^2 + 5 x < or equal to 2 3 - x^2 x > 2 find lim f(x) x -> 2^+ lim f(x) x -> 2^- lim f(x) x -> 2

*October 1, 2016 by Jessie*

**math**

the limit of cuberoot((-3x^3+5x+2)/(x^2-1)) as x approaches 3 is the problem. how could (-3x^3+5x+2) so it would be factored out with denominator? thanks! If you read the answer I gave for the previous question, then you can take the limit inside to get lim x->3 of((-3x^3+...

*September 3, 2006 by .*