01/31/14

Find the integral?
Find the integral of 3/((x-1)(x+2)) dx from 2 to 3.    Answer: ln(8/5)   I did partial fractions and got when x=-2, B=-1. And when x=1, A=1. What do I do next? Please show all your work.
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01/30/14

Find F'(x)?
If F(x)=∫ sqrt(1+t^3)dt from 1 to x^2, find F'(x).   Answer: 2x*sqrt(1+x^6)   Please show all your work.
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01/30/14

Find the limit?
Find the limit of (sin(x+h)-sin(x))/h as h approaches 0.   Answer: cos x   Please show all your work.
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01/29/14

Find the integral?
Find the integral of x(x^2+2)^2 dx from 0 to 1.   u=x^2+2 du=2x dx 1/2 du=x dx 1/2 ∫ u^2 du   What do I do next? The answer is 19/6. Please show all your work.
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01/29/14

Find the area?
Find the area of the region in the first quadrant enclosed by the graph of y=x(1-x) and the x-axis.    Answer: 1/6   Please show all work.
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01/28/14

Find its volume?
The base of a solid is the region enclosed by the graph of y=e^-x, the coordinate axes, and the line x=3. If all plane cross sections perpendicular to the x-axis are squares, find its... more
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01/26/14

Please help me with this problem?
Which of the following is the coefficient of x^4 in the Maclaurin series generated by cos (3x)?    a) 27/8 b) 9 c) 1/24 d) 0 e) -27/8   Please help me step by step. Show all your work. 
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01/26/14

Please help me with this problem?
If f(0)=0, f'(0)= 1, f"(0)=0, and f'''(0)=2, then which of the following is the third order Taylor polynomial generated by f(x) at x=0?    a) 2x^3+x b) (1/3)x^3+(1/2)x c) (2/3)x^3+x d)... more
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01/25/14

Can you help me with this AP Calculus problem?
The graphs of the polar curves r=3 and r=4-2sin(theta) are shown in the figure above. The curves intersect when theta=pi/6 and theta=5pi/6.   a) Let S be the shaded region that is inside the... more
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01/25/14

Find the limit?
Consider the differential equation dy/dx=y^2(2x+2). Let y=f(x) be the particular solution to the differential equation with initial condition f(0)=-1.   a) Find the limit of (f(x)+1)/sin(x) as x... more
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01/20/14

Find the general solution?
Find the general solution for the equation dy/dx+y=xe^-x.   Answer: y=(x^2/2)e^(-x)+Ce^-x   Please show all your work.
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01/20/14

Find this integral?
Find the integral of 3/x^2 dx from -1 to 1.    Answer: nonexistent   Please show all your work. 
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01/17/14

Find the volume?
The region in the first quadrant between the x-axis and the graph of y=6x-x^2 is rotated around the y-axis. The volume of the resulting solid of revolution is given by   a) ∫ pi(6x-x^2)^2 dx from... more
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01/14/14

Find an equation?
Find an equation of the line normal to the graph of y=x^3+3x^2+7x-1 at the point where x=-1.   y'=3x^2+6x+7 y'(-1)=4 m=-1/4 y(-1)=-6   What do I do next? Please show work.
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01/12/14

What are all values?
What are all values of x for which the series ∑ (x-1)^n/n from n=1 to infinity converges?   Answer: 0≤x<2   Please show your work step by step. I'm new to this topic.
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01/11/14

Find an antiderivative?
Find an antiderivative of f(x)=e^(x+e^x).   Answer: e^e^x.   Here's the work: f(x)=e^x*e^e^x u=e^x du=e^x dx   How should I set up the integral with this u-substitution? Please show all... more
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01/10/14

Find the area?
Find the area of the region enclosed by the polar curve r=sin(2θ) for 0≤θ≤pi/2.   Answer: pi/8   Please show all your work.
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01/09/14

Find the limit?
Find the limit of ∫ sqrt(x^5+8)dx from 1 to 1+h all over h as h approaches to 0.   Answer: 3   Please show all your work. Thanks.
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01/07/14

Find f(x)?
If ∫ f(x)sinx dx=-f(x)cosx+∫ 3x^2*cosx dx, find f(x).   Answer: x^3   Please show all your work.
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01/07/14

Find h(x)?
If f and g are twice differentiable functions such that g(x)=e^f(x) and g"(x)=h(x)e^f(x), find h(x).   a) f'(x)+f"(x) b) f'(x)+(f"(x))^2 c) (f'(x)+f"(x))^2 d) (f'(x))^2+f"(x) e)... more
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01/06/14

Which of the following functions?
Which of the following functions shows that the statement "If a function is continuous at x=0, then it is differentiable at x=0" is false?   a) f(x)=x^(-4/3) b) f(x)=x^(-1/3) c)... more
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01/06/14

Find all values of c?
Let f be the function given by f(x)=x^3-3x^2. Find all values of c that satisfy the conclusion of the Mean Value Theorem of differential calculus on the closed interval [0, 3].   I know that... more
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01/04/14

Find f(e^-1).
If f is the solution of x*f'(x)-f(x)=x such that f(-1)=1, find f(e^-1).   Answer: -2e^-1    
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01/03/14

Find the integral?
Given f(x)=x+1 for x<0, cos pi*x for x≥0, find ∫ f(x)dx from -1 to 1.   Answer: 1/2
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01/03/14

Find the area?
  Find the area of the region enclosed by the polar curve r=1-cos θ.   Answer: (3/2)pi
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