If A=1+r^a+r^2a+r^3a+.......................to infinity B=1+r^b+r^2b+................to infinity then find a/b=????? Is r^2a supposed to be r^(2a) or a*r^2? In other words, is the a part of the exponent? what the heck is that? exponents are like 2 cubed or 2 squared. 2
99,801 results
Math
Which describes the end behavior of the graph of the function f(x)=2x^35x^2+x? a. f(x) approaches infinity as x approaches negative infinity and f(x) approaches infinity as x approaches infinity b. f(x) approaches negative infinity as x approaches

Help me check my calculus answers
1. Which of the following functions grows the fastest as x goes to infinity?  2^x  3^x  e^x inf f(x)/g(x) = 5 show?  g(x) grows faster than f(x) as x goes to infinity.  f(x) and g(x) grow at the same rate as x goes to infinity.

Calculus check please
1. Which of the following functions grows the fastest as x goes to infinity?  2^x  3^x  e^x (my answer)  x^20 2. Compare the rates of growth of f(x) = x + sinx and g(x) = x as x approaches infinity.  f(x) grows faster than g(x) as x goes to infinity.

math;)
1. At which values of x does the graph of f(x)=cos x intersect the xaxis? Select all that apply. (2 answers) a. 0*** b. pi/2*** c. pi d. 3pi/2 e. 2pi 2. Which of the following represents the domain and range of y=tan x? a. domain: infinity

algebra 2
what is the domain in interval notation when the restrictions are x cannot = 2 and x cannot = 2? I got (infinity, 2) U (2,infinity) (infinity, 2) U (2, infinity) but my math teacher marked this as wrong

calculus A
A particle moves according to a law of motion s = f(t) = t3  12t2 + 21t, t 0, where t is measured in seconds and s in feet. v(t) = 3t^2  24t 21 a(t) = 6t  24 e) Find the total distance traveled during the first 8 s. i) When is the particle speeding up?

Precalc
Find an equation of a rational function that satisfies the given conditions. Vertical asymptote: x = 4 Horizontal asymptote: y = 0 Xintercepts: none Yintercepts (0, 1/4) Multiplicity of 1 Removable discontinuity: x = 1 End behavior: x > infinity, f(x)

Please check my Caclulus
1. Find all intervals on which the graph of y=(x^2+1)/x^2 is concave upward. A. (negative infinity, infinity) B. (negative infinity, 1) U (1, infinity) C. (negative infinity, 0) U (0, infinity) D. (1, infinity) E. none of these I got C. I found the second

math
If f(x)=x7 and g(x)=sqrt(4x), what is the domain of the function f/g? a. (infinity, 4) b. (infinity, 4] c. (4, infinity) d. [4, infinity) e. (4, 7) U (7, infinity)

Calculus Limits
Question: If lim(f(x)/x)=5 as x approaches 0, then lim(x^2(f(1/x^2))) as x approaches infinity is equal to (a) 5 (b) 5 (c) infinity (d) 1/5 (e) none of these The answer key says (a) 5. So this is what I know: Since lim(f(x)/x)=5 as x approaches 0,

calculus
lim t> infinity for sqrt(4t^25t1)/(2t3) I get infinity or infinity, but the real answer is 1. How does this occur?

Calculus
F(x)=(2x1)/ (x 3) Rewrite f(x) as a piecewise function. Then find the limit as it approaches positive infinity and negative infinity.

calculus
If f has domain [0, infinity) and has no horizontal asymptotes, then lim_(x>infinity) f(x) = infinity or lim_(x>infinity) f(x) = infinity. Can someone please clarify whether this statement is true or false? Thank you

Calculus
Sketch the graph of the function that has the following properties. f is continuous on (infinity, infinity). points: (1,2), (0, 0), (1,0) f'(x)>0 at (infinity, 1) f'(1)=0 f'(x)0 on (1, infinity) f"(x)0 on (0, infinity) I'm having trouble graphing

calculus  ratio test
Posted by COFFEE on Sunday, July 29, 2007 at 6:32pm. 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

Please check my Calculus
1. Find all critical values for f(x)=(9x^2)^⅗ A. 0 B. 3 C. 3,3 D. 3, 0, 3 E. none of these I got D. I found the derivative and solved for critical numbers. 2. Find all intervals on which the graph of f(x)=(x1)/(x+3) is concave upward A. (negative

Math
Identify the end behavior f(x)=(x4)^2 As x > positive infinity, f(x) > ____ infinity and as x >, f(x) > ____ infinity Fill in blank

Calculus
Which of the following series could be tested for convergence/divergence with the integral test? the summation from n=1 to infinity of 1/n! the summation from n=1 to infinity of 1/n the summation from n=2 to infinity of ln(n)/n^2 a) I only b) II only c) II

Please check my Calculus
1. Find all points of inflection of the function f(x)=x^46x^3 A. (0, 0) B. (0, 0), (9/2, 2187/16) C. (3, 81) D. (0, 0), 3, 81) E. none of these I got D. I found the second derivative and solved for x and plugged values into original function to get

Math
Find the domain of the function. Write your answer in interval notation. (If you need to enter ∞ or ∞, type INFINITY or INFINITY.) h(u,v) = sqrt(4u^2v^2) u^2+v^2 = ?

Calculus
Find the horizontal asymptote of f(x)=e^x  x lim x>infinity (e^x)x= infinity when it's going towards infinity, shouldn't it equal to negative infinity, since 0infinity =  infinity lim x> infinity (e^x)x= infinity

Math
What is the domain of f/g, given f(x)= x+2 and g(x)= x7? I was told this below, all real numbers EXCEPT 7 But My choices are this, (infinity,7) U (7,infinity) (infinity,7) U (7,infinity) (infinity,2) U (2,7)U (7,infinity) (infinity,infinity)

Math
f(x)=root sign, and inside that x2 and g(x)x7. Which of the following is the domain of the quotient function? A. (infinity,2] B. (infinity,7) U (7,infinity) C. [2,7) U (7,infinity) D. (2, infinity)

Algebra
Solve x(x7)(x9)

Algebra
Given f(x)=rootsignx2 and g(x) = x7 what is the domain of the quotient function? A. (infinity,2] B. )infinity,7 U (7, infinity) C. [2,7) U (7, infinity) D. (2,infinity) Responses

math
I'm working on solving and graphing inequalities. My problem is 1 < 6n + 3n I solve to get 1/9 < n When I graph and show my set, is it (1/9, infinity) or is it (0, infinity)? I thought it would be (1/9, infinity), but my teacher showed (0, infinity). On

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

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

Math
Limit = x>infinity 11x^5+4x^36x+2/6x^3+5x^2+3x1 My work: After doing lots of work I got 11/x^2 +4 6/x^2 +2/x^3 All over 6+5/x+3/x^21/x^3 So then I get 4/6 but the correct answer is supposed to be infinity.. I'm very confused

calculus
what is the answer for the integral of (1/(xln(x)) from 1 to infinity? I first found the integral using u substitution so u=ln(x) and du=1/x*dx this gave my du/u,leading to the ln(u) =ln(ln(x)) from 1 to infinity then I did the limit as t approaches

Algebra I
I'm stuck on this problem please help me find the range of this equation y = (x^2  4)/(x^2  x  12) I know that it is [1/3,infintiy]U[?,infinity] yes I'm having trouble with that ? At first I was like ok there should be a horizontal asymptote at y=1

Math
Richard shot a homemade rocket from a field behind is house. The height of the rocket, in feet, t seconds after it left the ground is shown in the function below. r(t) = 30t + 390t What is the domain of the height function? A. (infinity sign, infinity

Algebra
Find the domain of the function. Write in interval notation. sqrt(x^2 − 64). For the answer, I got (infinity, 8)u(8, infinity), but that's wrong, and I'm not sure what else to try?

MATH
I have been trying to do this problem for a couple of days but i cant seem to get the answer. Any help would be greatly appreciated. For each of the following forms determine whether the following limit type is indeterminate, always has a fixed finite

Math
Which statement correctly describes the end behavior of f(x) = 9x^4 + 3x^3 + 3x^2  1? As x goes to infinity, f(x) goes to infinity, and as x goes to negative infinity, f(x) goes to infinity. As x goes to infinity, f(x) goes to negative infinity, and as x

Algebra
f(x)=root sign, and inside that x2 and g(x)x7. Which of the following is the domain of the quotient function? A. (infinity,2] B. (infinity,7) U (7,infinity) C. [2,7) U (7,infinity) D. (2, infinity)

Algebra
Given f(x)=rootsignx2 and g(x) = x7 what is the domain of the quotient function? A. (infinity,2] B. )infinity,7 U (7, infinity) C. [2,7) U (7, infinity) D. (2,infinity)

Algebra
Given f(x)=rootsignx2 and g(x) = x7 what is the domain of the quotient function? A. (infinity,2] B. )infinity,7 U (7, infinity) C. [2,7) U (7, infinity) D. (2,infinity)

Math Please Check
Please tell me if this are right. Thank you! Find the exact location of all the relative and absolute extrema? h(t) = t^3  3t^2 domain: [1, + infinity) For this one I got x=2 as the minimum, and x=0 as the maximum. g(t) = 3t^4  16t^3 + 24t^2 +1 domain:

Algebra
I know what the answer is just not how to exopress it. Can someone help me please? State the domain of the function: f(x)(2+x)/(3x) Now I know the domain is (infinity,3) U (3, infinity)? (infinity,3] U [3, infinity) ? How do I express it? do I use ]

Algebra
I know what the answer is just not how to exopress it. Can someone help me please? State the domain of the function: f(x)(2+x)/(3x) Now I know the domain is (infinity,3) U (3, infinity)? (infinity,3] U [3, infinity) ? How do I express it? do I use ]

Algebra
What is the answer? I came up with C. is this correct? Thanks for the help in advance! f(x)=root sign, and inside that x2 and g(x)x7. Which of the following is the domain of the quotient function f/g? A. (infinity,2] B. (infinity,7) U (7,infinity) C.

Calculus 3
Determine whether the lines intersect(have a common point) and if so, find the coordinates of that point? r(t) = < 4t+3, 4t + 2, 6t + 6>, for infinity < t < infinity R(s) = < s + 2, 3s  1, 4s + 10>, for infinity < t < infinity And if r and R describe

Calculus
How do I find the radius of convergence of a series where n=1 to infinity of (14^(n)x^(n)n!)? I have tried using the ratio test but I eventually get to this step: lim as n approaches infinity of absolute value of (14x(n+1)), which equal infinity. How am I

Algebra
Solve 9 – 4x > 7 and write interval notation for the solution set. A.(1/2, 4) B. (4,1/2) C. (1/2, infinity) D. (infinity U (4, infinity) I say the answer is D..Am i correct?

Math
Let f:[0,infinity) > R be a differentiable function such that f'(x) >= f(x) > 0 for all x in [0,infinity). Construct a proof to show that f'(x) >= f(x) for all x in [0,infinity).

Algebra
please check my answers. thanxs! Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. x^2  6x + 5 > 0 I got (ininity,1) u (5, infinity) x^2  3x  18 < 0 I got (infinity,3) u (6,

math
if the inequality is: (x+5/x2)>0 . "x5 over x2 greater or equal to 0". What would be the solution? a.(infinity sign, 5] U (2, infinity sign) b.(5,2) c.(infinity sign, 5) U [2, infinity sign) d.[5,2] My answer was C. Am I correct?

math
What is the domain of the function f(x)=11/Squareroot of 4x^2 a.(11,11) b.[11,11] c. (2,2) d. [2,2] What is the range of the function? y=8/Squareroot of 4x^2 a. [4, infinity) b. (infinity, 4] c. [8, infinity) d. (infinity, 12] e. [6, infinity) f.

Math
Find the limit if it exists. lim 1/(x2) = infinity x→2+ lim 1/(x2) = negative infinity x→2 lim 1/(x2) = 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?

Algebra
Can you please check my answers? Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. x2/x+1 or equal to 0 my answer: (3,8] 2/x2

Math
A particle P starts at the origin (x0,y0)=(0,0), of the plane. The particle moves in steps as follows. 1. P moves 1 unit to the right to the point (x1,y1)=(1,0), then 2. P moves 1/2 unit up to (x2,y2)=(1,1/2), then 3. P moves 1/4 unit to the left to

Algebra
Given f(x)=rootsignx2 and g(x) = x7 what is the domain of the quotient function? A. (infinity,2] B. )infinity,7 U (7, infinity) C. [2,7) U (7, infinity) D. (2,infinity)

calculus  interval of convergence
infinity of the summation n=0: ((n+2)/(10^n))*((x5)^n) .. my work so far. i used the ratio test = lim (n>infinity)  [((n+3)/(10^(n+1)))*((x5)^(n+1))] / [((n+2)/(10^n))*((x5)^n)]  .. now my question is: was it ok for me to add "+1" to "n+2" to become

BC Calculus
lim x >infinity (e^x/lnx) I got infinity/0 but is that allowed to be my answer? what about this one: limx>infinity (sqrt of x /e^x) i got 0/infinity for this.

Math
I am supposed to figure out what this rational function is by using these clues and I am a little confused. Can someone please explain how I do this? asymptotes: horizontal~none vertical~x=4 slant~y=x+1 end behavior~ f(x) approaches infinity as x

calculus  interval of convergence
infinity of the summation n=0: ((n+2)/(10^n))*((x5)^n) .. my work so far. i used the ratio test = lim (n>infinity)  [((n+3)/(10^(n+1)))*((x5)^(n+1))] / [((n+2)/(10^n))*((x5)^n)]  .. now my question is: was it ok for me to add "+1" to "n+2" to become

Math
1. If 1/infinity = infinity or infinity ? 2. If lim x>infinity^ = infinity & lim x>inifinity^+ = infinity, then lim x>infinity = does not exist. Am i right? If im wrong please tell me the reason why?

Math
1. If 1/infinity = infinity or infinity ? 2. If lim x>infinity^ = infinity & lim x>inifinity^+ = infinity, then lim x>infinity = does not exist. Am i right? If im wrong please tell me the reason why?

Calculus
find the intervals where the function is increasing and the intervals where it is decreasing f(x)= (x^3/3)(x^2/2) ok i found its derivative which is (f1(x)=(x1)x my options are increasing a) (0,infinity) b) (1,0) c(infinity,0)U(1,infinity) decreasing

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)) 

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

Calculus
Determine convergence or divergence for the following series. State the tests used and justify your answers. Sum (infinity, n=1) 1/(1+e^n) Sum (infinity, n=1) (2*4*6...2n)/n! Sum (infinity, n=0) (n6)/n Sum (infinity, n=0) (n6)/n! Sum (infinity, n=0)

Math
Consider the equation below. (Round the answers to three decimal places. If you need to use infinity or infinity, enter INFINITY or INFINITY.) f(x) = 9 sqrt(xe*^(x) (a) Find the interval on which f is increasing. ( , ) Find the interval on which f is

Algebra
Given f(x) = ãx  2 and , which of the following is the domain of the quotient function ? a.(infinity,2] b.(infinity,7) U (7,infinity) c.[2,7) U (7, infinity) d.(2, infinity)

ALGEBRA
Solve the inequality. (Enter INFINITY for infinity and INFINITY for infinity as needed.) 3

ALGEBRA
Solve the inequality. (Enter INFINITY for infinity and INFINITY for infinity as needed.) 9x>=4 x + 34

ALGEBRA
Solve the inequality. (Enter INFINITY for infinity and INFINITY for infinity as needed.) 6

Calculus
I've been trying to solve the improper integral of ln(x)/sqrt(x) dx as a=1 and b=infinity I am required to solve for this question and according to my answer, it is divergent. However, my answer is infinity4. Is it acceptable to say that infinity minus a

Mathintergration
Show that integrate.[e^(4x)*(cos 3x)] from 0infinity =4/25 I got the answer(without applying limits) as, {(e^(4x) )[3sin(3x)  4cos(3x)]}/25 But when applying the upper limit what is the value of, {(e^(infinity) )[3sin(3*infinity) 4cos(3*infinity) ]

Algebra
Convert these solutions into an inequality A)[3, infinity) b)(infinity, 2] U (3,18) C)(infinity, 5] U (8, infinity)

pre algebra
what is the domain of the function below? f(x)= x^2 + 11 thank you choices are: 1. ( infinity, 11) 2. (infinity, infinity) 3.(11, 11) 4. (11, infinity)

calculus
We were asked to solve the problem 1/x < 4. I solved it like so: 1

calculus
State which of the conditions are applicable to the graph of y = f(x). (Select all that apply.) lim x→infinity f(x) = −infinity lim x→a+ f(x) = L lim x→infinity f(x) = L f is continuous on [0, a] lim x→infinity f(x) = 0 f(a) is not defined lim

Inequality
please check my answers. thanxs! Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. x^2  6x + 5 > 0 I got (ininity,1) u (5, infinity) x^2  3x  18 < 0 I got (infinity,3) u (6,

Precal
Please determine the following limits if they exist. If the limit does not exist put DNE. lim 2+6x3x^2 / (2x+1)^2 x>  infinity lim 4n3 / 3n^2+2 n> infinity I did lim 2+6x3x^2 / (2x+1)^2 x>  infinity (2+6x3x²)/(4x²+4x+1) (2/x² + 6/x 3)/(4 + 4/x

Math
a) Find the zeros of the function. d) Find the domain. e) Find the range. a) none d) (infinity, 0) U (2,infinity) e) (0, infinity) Is this right?

college algebra
now i understand both intersection and union but not with an infinity. how do i figure this out (infinity,4)n(0,infinity)

Please check my Calculus
1. Find the value(s) of c guaranteed by Rolle’s Theorem for f(x)=x^2+3x on [0, 2] A. c=3/2 B. c=0, 3 C. Rolle’s Theorem doesn’t apply as f is not continuous on [0, 2] D. Rolle’s Theorem doesn’t apply as f(0) does not equal f(2) E. None of these

Calculus
I am maybe overthinking this, but what is the lim as n> infinity of (n+1)/(n+2) ? I am trying to use the ratio test to find interval of convergence for the infiinite series (n/n+1)((2x)^(n1)) so i did the limit of (n+1)/(n+2) but i am wondering if

Piecewise function
write a piecewise function over 3 intervals whose domain is (infinity, infinity) and whose range is (infinity,3) united (1,10). include an increasig, decreasing, and a constant function.

Calculus
For f(x)=(3x^25x+2)/(2x^26) complete the statements. f(x)>_________ as x>infinity f(x)>_________ as x>infinity In the blanks, I say for the first one infinity then infinity for the second one.

Math
The sum to infinity of a G.P. is 16 and the sum of the first 4terms is 15. Find the first 4 terms. Find the sum to infinity of the following (if they converge). ?(a)4+4/3+4/3²+... (b)9+7+5+3+...(can't do, its an AP ?) (c)2010+52.5+...a=20,r=0.5

math
i really don't understand why this 1lim 3/(y+4) [the lim is x>infinity] the ans is 0 while this 2lim (76x^5)/(x+3) [x>+infinity ] is  infinity. can anyone explain why the 1 is zero & the 2 is infinity.

Calculus
The limit from x> infinity of x^(3/x) i keep getting 3/infinity, which is infinity and this answer is incorrect.

Calculus
Which of the following series converge? A. ∑n=1 to infinity of 1/n^2 B. ∑n=1 to infinity of 1/n C. ∑n=1 to infinity (1)^n/(√n) I think the answer is A and C.

calculus please help
the actual problem is integral(2 to +infinity) (1/x^2) dx and after integrating and plugging in the bounds, i got 1/(infinity sign)+ 1/2 does that converge to 1/2, Ln2, 1, 2 or is the answer nonexistent? what i was thinking that everytime the bottom

MathCalculus
Hi, I am trying to figure out what the limit as h approaches 0 of (12h)^(1/h) is. I am unfamiliar with the process I am supposed to use to solve this limit. I have just been reasoning out this limit, but I keep getting the answer, 1^(infinity)=1. My

Rational Inequities
Can you please check my answers? Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. x2/x+1 or equal to 0 my answer: (3,8] 2/x2

Calculus
F(x)=(2x1)/ (x 3) Rewrite f(x) as a piecewise function. Then find the limit as it approaches positive infinity and negative infinity.

calculus
f(x)=2x+8x^1.For this function there are four important intervals: (infinity,A],[A,B),(B,C), and [C,infinity) where A,B and C are either critical numbers or points at which f(x) is undefined.Find A,B and C.

calculus
Recall that a function G(x) has the limit L as x tends to infinity, written lim(x>infinity)G(x) = L, if for any epsilon > 0, there exists M >0 so that if x > M, then G(x) − L < epsilon. This means that the limit of G(x) as x tends to infinity does not

math (3)
Find the domain of the function. Write your answer in interval notation. (If you need to enter ∞ or ∞, type INFINITY or INFINITY.) f(s,t)= sqrt(s^2+t^2) s = ? t = ?

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)) 

ALGEBRA
Solve the inequality. (Enter INFINITY for infinity and INFINITY for infinity as needed.) 6

Math
For the graph of (3x)/(5x+2)^3: is the following information right? xintercept: (3,0) yintercept: (0,0.375) vertical asymptote: x= 0.4 horizontal asymptote: y=0 increasing: (4.7, infinity) decreasing: (infinity, 0.4) (0.4, 4.7) concave up: (0.4,

Precalculus
Can somebody help me wit this? Find the range and the domain of: f(x)=(1/2)x2 The domain is all real numbers (x) from infinity to infinity The range (of f(x)) is 0 to infinity, since it can never be negative. f(x) has a minimum value of zero when x=2.

Math
The function f(x)=(x1)/(x4)*sqrt(x+2) is negative for x in... a. (1,4) b. (infinity, 4) c. (infinity, 1) d. (4, infinity)

Calculus
Find the limit. lim 1/x^24 a)x>2^+ b)x>2^ c)x>2^+ d)x>2^ I'm completely lost. I don't understand how some answers are infinity and the others are negative infinity.

math (4)
Find the domain of the function. Write your answer in interval notation. (If you need to enter ∞ or ∞, type INFINITY or INFINITY.) h(u,v) = sqrt(4u^2v^2) u^2+v^2 = ?