# calculus - limits

17,658 results

### Calculus

We are doing limits in Calculus, but now we are doing trig limits too and i do not get how to do any of them. For example ones like this, how do you do them? sec (x-1) / (x sec x) x approaches 0 ((3 sin (x)) 1 - cos(x)) / (x^2) x approaches 0 (sin (2x)) / (sin (3x)) x ...

### calculus (limits)

Use limits to explain why f(x)= (7-3X)/(X+9) has a vertical asymptote.

### Maths Calculus Derivatives & Limits

Using the definition of the derivative evaluate the following limits 1) Lim h---> 0 [ ( 8 + h )^1/3 - 2 ] / h 2) Lim x ---> pi/3 ( 2cosx - 1 ) / ( 3x - pi)

### Calculus

TWO examples of each of the following: two sided limits and theorem on limits (SUM, difference, product, quotient, nth root, ).

### Math

I'm in Calculus AP and we are learning about limits. I'm having trouble with finding limits algebraically. So here's a sample that you can use to help explain this to me. Find the limit of lim x (arrow to the right) 1 x-1/x(squared)-1. Please help!

### AP Calculus

Find each of the limits without a calculator. Use the limits as an aide to sketch the graph of f(x)= (x-2)/(|x|-2) for-10<_x<_10 and -6<_y<_6. Be sure to clearly indicate any asymptotes, holes or other important characteristics. lim x->∞ f(x)

### Calculus

TWO examples of two sided limits and each theorem on limits.

Combine the following two integrals into one by sketching the region, then switching the order of integration. (sketch the region) im gonna use the S for integral sign..because idk what else to use. SS6ycos(x^3-3x)dxdy+SS6ycos(x^3-3x) And the first integration limits for x are...

### math (Calculus III)

In this example we should use the beta function. But I'm a bit lost, because I don't know how to change the limits of the integral to fit the one that is needed when using B-function. The problem goes like this: integrate cos^7(x) dx, limits of the integral are from 0 to pi.

### Calculus 1

Write a function that has two infinite limits at two different x-values. Write a function where both one sided limits exist at some x value but the two sided limit do not. I don't understand how this would look, please help!

### Calculus

Apply the concepts of calculus (limits and derivatives) to describe the graph y = sec(x). Include a quality graph

### Calculus (Limits)

Let f be defined as follows, where a does not = 0, f(x) = {(x^2 - 2a + a^2) / (x-a), if x does not = a 5, if x = a Which of the following are true about f? I. lim f(x) exists as x approaches a II. f(a) exists III. f(x) is continuous at x = a. A. None B. I, II, and III C. I ...

### Calculus

Find the Limits. lim [t^3 + 3t^2]/[t^3 - 4t^2] t->0

### Math - Calculus

how to solve limits?

### 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...

### 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...

### Calculus

Using the first of these limits, find f'(3) if f(x)=4x^2+4x-2

### Calculus

Evaluate the following limits (x^2 + 2x - 8)/x-2 Lim x->2

### Calculus

Show, using limits, that f(x) = x2 – x + 3, is continuous at x = 2.

### Calculus - Limits

lim x--> 3 (3 - x)/ (x^2 - 9) I know the answer is -1/6, but I can't figure out how to get there.

### calculus

Evaluate the Integral ∫1, 0 x^3(1+x^4)^6dx where 1=b 0=a for the limits

### Calculus

Find the indicated limits. Lim x-> 1- sqrt 1 - 1/ x-1

### Calculus 1

Find the derivative of f'(x) of f(x)=4sqrt(x) using limits

### Calculus

Determine the following limits if it exists. a. lim x-->5 (4x/x-5)

### Calculus

Determine the following limits if it exists. a. lim x-->5 (4x/x-5)

### Calculus

determine all asymtote(s) of f(x)= 1/(x(x-1)^2) using limits

### calculus - limits

limit as x approaches infinity; tan^(-1) (x^2 - x^4) any help is appreciated =D

### calculus - limits

Does the limit lim 2011t/3-(squareroot)t+9 exist ? t-0

### Calculus (Limits)

f(x) is a function differentiable at x=1 and f′(1)=1/13. What is the limit of (x^3 - 1)/f(x) - f(1) as x approaches 1?

### u.s. history

How does the constitution limit the powers of government? A. The constitution limits the power of government by entitling citizens to a basic standard of living. B. The constitution limits the power of government by giving citizens the power to veto any bill they do not ...

### calculus - limits

can someone help me determine that limit for the following function, as x --> -2? 2 - abs(x) / 2 + x

### calculus

find the derevative (hint try to use limits) (x^2010 - 1 )\(x -1 )

### calculus

find the derevative (hint try to use limits) (x^2010 - 1 )\(x -1 )as x approaches1

### calculus-limits

For f(x) = e^x sinx , what can be said about lim x -> negative infinty? Explain.

### calculus

Find the total area enclosed by the functions given below. y=x^2+2x+1 and y=2x+5 limits are -2 to 2

### Calculus, Limits

Find the limit. lim t → ∞ (sqrt t + t^2)/(6t − t^2)

### Statistics

Multiple Choice Which of the following statements is true about the 95% confidence interval of the average of a sample? A) 95 of 100 avgs of samples will be within the limits of the confidence interval. B) There is a 95% chance the avg of the population to be within the limits...

### calculus

Given the function: y = 2 - x - x^3 use limits to find the slope (and then the equation) of the tangent line at x =2.

### calculus

Given the function y = 2 - x - x^3 Use limits to find the slope (and then the equation) of the tangent line at x = 2

### CALC-LIMITS

F(X)= x-2/(x^2-4) is continuous at x=1 and why as limits approach from 1+ and 1-

### Calculus

Evaluate the triple integral _E (xy)dV where E is a solid tetrahedron with vertices (0,0,0), (4,0,0), (0,1,0), (0,0,4) I just can't seem to find the limits, of x,y and z

### calculus, limits, l'hopital

Find the limit as x->0 of (2-2cos(x))/(sin(5x)) Mathematically I got 2/5, but on the graph it appears to be 0.

### Calculus

Use the definition of continuity and properties of limits to show that the function is continues at given a. f(x)=x^2+sqrt(7-x) a=4

### calculus

Rotate the region enclosed by the given functions around the x-axis. Determine the volume. y=x^2+2x+1 and y=2x+5 limits are -2 and 2

### college calculus

I don't know how to solve this indefinite integral with both limits as variables: ^x^3 ç (z^4+1)dz ⌄ln(x) If you could explain I'd appreciate it.

### calculus

For each of the following limits, determine the indicated limit if it exists. lim f(x)=? x approaches 4 from the left f(x)= -3.9997

### calculus

in your own words, describe how limits can be used to find the instantaneous rate of change of a function.

### calculus

Evaluate the limits without using a calculator. Justify all steps in the solutions. lim x-->0 x^7cos(3/x)

### calculus

Evaluate the limits without using a calculator. Justify all steps in the solutions. lim x-->0 x^7cos(3/x)

### Calculus

I am trying to solve the following L'hopital's limits question below: lim x -> 0 from the positive direction of ( 5^(sin(x)) - 1 )/ (x)

### calculus

Rotate the region enclosed by the given functions around the x-axis. Determine the volume. y=sqrt(sinx) ; y=0 ; x=0 ;x=pi limits are 0 to pi

### Calculus II: Finding the volume of a revolution

Question: Find the volume of revolution bounded by y-axis, y=cos(x), and y=sin(x) about the horizontal axis. Since the rotation is happening at the horizontal axis, I thought the limits of integration would be [-1,1] and if the curves are rotated they would over lap so i used ...

### double integrals

Combine the following two integrals into one by sketching the region, then switching the order of integration. (sketch the region) im gonna use the S for integral sign..lol SS6ycos(x^3-3x)dxdy+SS6ycos(x^3-3x) And the first integration limits for x are between -1 and y, for y ...

### Math - Arithmetic question

I have a question about the limits to Arithmetic problems, on my homework I've noticed that so far all of the arithmetic sequences limits are infinite (-infinity or +infinity, I was just wondering if all the limits to Arithmetic problems are to an infinity since 99% of the ...

### Maths (limits)

how do i evaluated these limits: lim x --> 3 ((square root of x^2 +16)- 5)/(x^2 - 3x) lim x--> to infinity (2+ 100/x)

### AP Calc (Limits on Piecewise Functions)

I'm trying to find the left, right, and overall limits of this function without using a calculator. Any help/suggestions on how I'm supposed to do this would be very helpful! f(x){ sinx if x<pi/6 tanx if x=pi/6 a=pi/6 cosx if x>pi/6

### Calculus (limits)

The question is to "state the value of each quantity, if it exists." We are given a piecewise function that is graphed, and no equation. What does it mean when we're asked to find f(2)?

### Math (Stats)

What is the difference between class limits and class boundaries? A) Class limits are the numbers that separate classes without forming gaps between them. Class boundaries are the least and greatest numbers that can belong to the class. For integer data, the corresponding ...

### AP Calc (Limits on Piecewise Functions) #2

I need help trying to find the left, right, and overall limits for this piecewise function without using a calculator. f(x) = { sin(x/3) if x≤pi , (x√ 3)/(2pi)if x>pi} when a=pi

### Calculus

I'm not sure how to calculate limits from graphs. I've tried many times but I can't figure it out. Are there any sites or tips you can give me? Thank you very much, I really appreciate it.

### Calculus

May someone answer this question for me? Thank you! I appreciate it. a.) Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval. f(x)=(2x+3)/(x-2), (2, ∞)

### calculus

f(x)=−x3 −x2 +16x+16 1. Calculate f′(x). 2. Calculate f′′(x). 3. Find the x values such that f(x) = 0. Note: this can be done by factoring. 4. Find the stationary point/s. Note: a point requires x and y coordinates. 5. Determine the nature of this/these point/s. 6. ...

### Calculus I - Limits

How do I find lim x-> infinity √(x^2 + x) - √(x^2 - x)

### calculus

Compute each of the following limits if they exist. lim 3x^(2)-x-2 x->2 lim (x^(2)+x-6)/(x-2) x->2

### Calculus

Find the limits if they exist lim_x->0 x/|x| lim_x->0+ sqr(x+4)

### Calculus

Show, using the properties of limits, that if lim x-->5 f(x)=3 then lim x---->5 x^2-4/f(x)=7

### Math Limits

(x^n-1)/((x-1) )=(x-α^1 )×(1-α^2 )×………..(x-α^((n-1)) ) How do we prove that n = the multiplication of the second term using limits and l'hopital's rule.

### calculus

I don't know if I'm typing it in wrong into my graphing calculator but I need to estimate the limits of sin(8 theta) / theta

### Calculus

Use Riemann sums and limits to compute the area bounded by f(x) = 10x+9 and the x axis between x=10 to x =5 The area is = to

### Calculus

1. Use a graph to estimate the limit. Use radians unless degrees are indicated by θ°. (Round your answer to four decimal places.) lim θ → 0 θ/tan(7θ) 2. Assuming that limits as x → ∞ have the properties for limits as x → c, use ...

### Calculus ( finding limits)

Find the limit as x-->-inf (x+2)^(3/2)+1 ----------I know that the answer is infinity but I don't know how to get this answer by hand. Could someone please help me? Thanks a lot!

### Calculus

Hey, we covered limits at the beginning of the year, but I cannot remember how to do them at all. >>>what is the limit, as x approaches 2, of ((1/x )-(1/2))/(x-2)? Please go step by step!

### calculus

Find the limits Lim(sin kt/t) t approaches 0 and (K is constant) How do you start this and go about it stepwise? Does knowing (K constant) help me to solve this?

### Calculus

F(x)=|x-5| evaluate the following limits lim x->5- ( f(x)-f(5))/(x-5) lim x->5+ ( f(x)-f(5))/(x-5)

### Calculus

Let R be the region bounded by the curve x=9y-y^2 and the y- axis. Find the volume of the solid resulting from revolving R about the line y= -6. I believe the integral limits are from y=0 to y-9 i set up h(x) = 9y-y^2 r(x) = y+6 I am not sure if this is correct Can anyone help...

### Calculus

lim(x->infinity) sqrtx sin(1/sqrtx) Someone please start me off. I don't know how to find the limits of trigonometric functions.

### calculus (limits)

lim h>0 sqrt(1+h)-1/h not sure how to factor this; not allowed to use L'Hopital's Rule. (that isn't taught at my school until Calc II & I'm in Calc I).

### Calculus 1

Find the instantaneous velocity, using limits, for the given value of t of an object moving according the given equation. a. s(t)=t^2–8t+18 ; t=3 b. 𝑠(𝑡)=1/t^2 ; t=1

### Calculus

I need some help on getting ideas for my limits & continuity calculus project! For the limits project: I have to conduct an "interview with a limit" (Q&A format).I have to include factual information like definitions, properties, theorems, etc. I also have to include sketches...

### calculus

Evaluate the following limits after identifying the indeterminate form. Use Hospital's rule. d) lim x_0+ (xe^(2x) + 1)^(5/x) e) lim x_(Pi/2)+ (1 + sec3x)^(cot3x) Thank you!

### Calculus 1

Evaluate the following limits after identifying the indeterminate form. Use Hospital's rule. d) lim x_0+ (xe^(2x) + 1)^(5/x) e) lim x_(Pi/2)+ (1 + sec3x)^(cot3x) Thank you!

### calculus

Find the limits lim_x->2 x^3+x lim_x->2 (x^2-4)/(x-2)

### Calculus/College Algebra

I'm so lost. We're working on limits for this assignment and I get that, but my difficulty lies in breaking down the original problem. The problem is: Find the limit: lim (x->5) The numerator is (the square root of 9-x) -2 and the denominator is x-(the square root of x+20...

I asked this question on last thursday and u told me that the bottom limit for the 1st and the right limit for the 2nd area is missing? The question that i posted had no other information and i don't know why you said that the limits are missing. There is no other limits that ...

### Legal Environment of Bus

Ethics Question (Legal Environ of Bus)? Various industries have lobbied for legislative restrictions on tort liability. The nuclear power industry has long been protected by a statute that limits its upper-dollar liability in the event of a serious accident. Many companies in ...

### Calculus-limits

I'm studying for the AP exam and I can't figure this problem out. I thought the answer was negative infinity but that isn't an option. Thank you in advance! What is the limit as x approaches infinity of (9x-x^2-7x^4)/(x^3+12x)? a. 9 b. 7 c. -7/12 d. -7 e. Does not exist

### Absolute Value and Limits

solve for limits of 1+ and 1- for this function: (x^2 + abs (x-1) - 1)/ abs (x-1) i don't know how to simplify abs. value expression times polynomial. can someone please help.

### consumer math

amy miller's insurance policy has a \$218.00 premium for 25/100 bodily injury limits and \$25,000.00 property damage limits. the collision premium is \$74.00. amy's driving-rating factor is 2.4. what is her annual premium?

### Calculus-Limits

i have no clue how to start it. rationalizing it seems to tedious. how do i do this thanks evaluate the limit as h -> 0 ((fourth root(3 + h) - 2(3+h) - fourth root(3) + 6))/h

### calculus - limits

In the theory of relativity, the mass of a particle with velocity v is m = m0 / sqrt(1-v^2 / c^2) where m0 is mass of the particle at rest and c is the speed of light. What happens as v approaches c^-?

### 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.

### Calculus

How would you find the derivative of f(x)=1/sqrtx using limits? I know how to do problems with a fraction or a square root, but I can't figure out how to do one with both. I have tried a few different starts, but always end up getting stuck.

### Calculus

Determine the limit of the trigonometric function: Limit as x approaches pi/4 of (1-tanx)/(sinx-cosx) I need step by step help using the special trignometric limits theorem.

### Calculus

find the value of a, if it exists, such that the following function is continuous at X = 2. piecewise function f(x)={x^2-3x+1, if x>2; a, if x=2; 3-2x, if x<2 I found the limits from left and right of 2 = -1 so the limit exists but I don't know how to figure out a

### stats

4. Data from the 2008 General Social Survey (GSS) sample show that the mean number of children per respondent was 1.94 with a standard deviation of 1.70. A total of 2,020 people answered this question. (a) Estimate the population mean number of children per adult using a 90% ...

Assuming that limits as x → ∞ have the properties for limits as x → c, use algebraic manipulations to evaluate lim x → ∞ for the function. a. f(x) = x − 2/2 + 6x^2 b. f(x) = x^2 + 6/x + 7 Please help! I do not know how to start with this ...

### 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

### 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+...

### Calculus

Hello all, I would like some confirmation on a limits question. The limit is as h --> 0, [sqrt [73-5(x+h)] - sqrt (73-5x)]/h I multiplied by the conjugate of the numerator and reduced everything down to this final answer: [(-5)sqrt(73-5x)]/2 Is this correct?

### calculus, limits, l'hopital

Using l'hopital's rule, find the limit as x approaches infinity of (e^(6/x)-6x)^(X/2) I know l'hopital's rule, but this is seeming to be nightmare. I just don't seem to get anywhere.