04/06/14

Can you answer this calculus question?
A particle starts at time t=0 and moves along the x-axis so that its position at any time t≥0 is given by x(t)=(t-1)^3*(2t-3).    a) For what values of t is the velocity of the particle less than... more
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04/06/14

Can you answer this calculus question?
A particle moves on the x-axis so that its velocity at any time t≥0 is given by v(t)=12t^2-36t+15. At t=1, the particle is at the origin.    a) Find the maximum velocity of the particle for... more
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04/06/14

Find the radius of convergence?
Find the radius of convergence of the power series ∑ (-1)^n*(4x+1)^n from n=0 to infinity.    Answer: 1/4   I did the ratio test and got limit as n approaches to infinity of absolute value of... more
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04/06/14

Find the radius of convergence?
Find the radius of convergence of the power series ∑ x^n from n=0 to infinity.    Answer: 1   I did the ratio test and got limit as n approaches to infinity of absolute value of x^(n+1) divided... more
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04/05/14

Find the integral?
Find the integral (2x-1)/(x-1)^2 dx.   Please show all your work. Thanks.
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04/04/14

Which of the following is the radius?
Which of the following is the radius of convergence of the series ∑ (n(2x-5)^n)/(n+2) from n=0 to infinity?   a) 1 b) 1/2 c) 3/2 d) 2 e) 5/2   I worked the problem and the answer I got is... more
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04/03/14

Can you answer this calculus question?
Let f(x)=∑ x^n from n=0 to infinity. The radius of convergence of ∫ f(t) dt from 0 to x is   a) 0 b) 1 c) 2 d) ∞ e) none of these   Answer: B   Please show all your work.
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04/03/14

Can you answer this calculus question?
The series ∑ n!(x-3)^n from n=0 to infinity converges if and only if    a) x=0 b) 2<x<4 c) x=3 d) 2≤x≤4 e) x<2 or x>4   Answer: C   Please show all your work.
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04/03/14

Which of the following sequences diverges?
Which of the following sequences diverges?   a) an=1/n b) an=((-1)^(n+1))/n c) an=(2^n)/(e^n) d) an=(n^2)/(e^n) e) an=n/ln(n)   Answer: E   n after an is lower case.   Please show all... more
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04/02/14

Please answer this calculus question?
Let f be the function defined by f(x)=∑ 2((x+2)/3)^n from n=0 to infinity for all values of x for which the series converges.    a) Find the interval of convergence for the series.  b) Find the... more
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04/01/14

Which of the following?
Which of the following functions grows at the same rate as e^x as x-->infinity?   a) e^2x b) e^3x c) e^(x+2) d) e^-x e) e^(-x+1)   Please show all your work.
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04/01/14

Which of the following?
Which of the following is the sum of the series pi^n/e^(2n) from n=0 to infinity?    a) e/(e-pi) b) pi/(pi-e) c) pi/(pi-e^2) d) e^2/(e^2-pi) e) The series diverges.    Answer: D   Please... more
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04/01/14

Which of the following?
Which of the following is the quadratic approximation for f(x)=e^-x at x=0?    a) 1-x+(1/2)x^2 b) 1-x-(1/2)x^2 c) 1+x+(1/2)x^2 d) 1+x e) 1-x   Answer: A   Please show all your work. Thanks.
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03/31/14

Which of the following?
Which of the following gives the Taylor polynomial of order 5 approximation to sin(1.5)?   a) 0.965 b) 0.985 c) 0.997 d) 1.001 e) 1.005   Please show all your work. 
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03/31/14

Write the volume of the solid?
The infinite region in the first quadrant bounded by the coordi-nate axes and the curve y=1/x-1 is revolved about the y-axis to generate a solid.    Write the volume of the solid as an improper... more
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03/30/14

Find the integral?
Find the integral of (2 dx)/(x^2-2x) from 3 to infinity.   Please show all your work.
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03/30/14

Please answer this calculus question?
Consider the region R in the first quadrant under the curve y=(2*ln(x))/x^2.    a) Write the area of R as an improper integral. b) Express the integral in part (a) as a limit of a definite... more
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03/30/14

Please answer this calculus question?
The second and fifth terms of a geometric sequence are -4 and 1/2, respectively. Find   a) the first term, b) the common ratio, c) an explicit rule for the nth term, and d) a recursive rule... more
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03/30/14

Which of the following?
Which of the following gives the value of the area under the curve y=1/(x^2+1) in the first quadrant?    a) pi/4 b) 1 c) pi/2 d) pi e) diverges    Please show all your work.
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03/29/14

Which of the following?
Which of the following is the limit of the sequence with nth term an=(-1)^n*(3n-1)/(n+2)?    a) -3 b) 0 c) 2 d) 3 e) diverges   Please show all your work. 
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03/29/14

Find the limit?
Find the limit of 3x^(2x) as x approaches to 0+.    Please show all your work. 
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03/28/14

For what values of t?
The temperature outside a house during a 24-hour period is given by F(t)=80-10cos(pi*t/12), 0≤t≤24, where F(t) is measured in degrees Fahrenheit and t is measured in hours.    Question:   An... more
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03/28/14

Which of the following?
The second and third terms of a geometric sequence are 2.5 and 1.25, respectively. Which of the following is the first term?    a) -5 b) -2.5 c) 0.625 d) 3.75 e) 5   Please show all your... more
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03/28/14

Which of the following?
Which of the following is the limit of the sequence with nth term an=n*sin(3pi/n)?   a) 1 b) pi c) 2pi d) 3pi e) 4pi   The n for an is lower case. Do I supposed to take the limit as n... more
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03/28/14

Which of the following?
The first and third terms of an arithmetic sequence are -1 and 5, respectively. Which of the following is the sixth term?    a) -25 b) 11 c) 14 d) 29 e) 3125   Please show all your work.
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