03/27/14

Which of the following?
Which of the following expressions should be used to find the length of the curve y=x^(2/3) from x=-1 to x=1?   a) 2*∫ sqrt(1+(9/4)y) dy from 0 to 1   b) ∫ sqrt(1+(9/4)y) dy from -1 to... more
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03/27/14

Which sequence converges?
Which sequence converges?   a) an=n+3/n   b) an=-1+(-1)^n/n   c) an=sin (n*pi)/2   d) an=n!/3^n   e) an=n/(ln(n))   I know that I have to take the limit as n approaches infinity and see... more
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03/26/14

The volume of the solid in cubic?
The base of a solid is a circle of radius 2 inches. Each cross section perpendicular to a certain diameter is a square with one side lying in the circle. The volume of the solid in cubic inches... more
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03/26/14

Which of the following?
Which of the following gives the length of the path described by the parametric equations x=(1/4)t^4 and y=t^3, where 0≤t≤2?   a) ∫ t^6+9t^4 dt from 0 to 2   b) ∫ sqrt(t^6+1) dt from 0 to... more
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03/26/14

Which of the following?
The length of a curve from x=0 to x=1 is given by ∫ sqrt(1+16x^6) dx from 0 to 1. If the curve contains the point (1, 4), which of the following could be an equation for this curve?    a)... more
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03/26/14

Find the integral?
Find the integral of (cos(2x) dx)/(sin^2 (2x)) from pi/12 to pi/4.    Answer: 1/2   Please show all your work.
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03/25/14

Help me with Calculus question?
At any time t≥0, the velocity of a particle traveling along the x-axis is given by the differential equation dx/dt-10x=60e^4t.    Find the general solution x(t) for the position of the... more
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03/25/14

Please help me with Calculus?
Let f be a function such that f"(x)=6x+8.    Find f(x) if the graph of f is tangent to the line 3x-y=2 at the point (0, -2).     
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03/24/14

Find the average value?
Find the average value of y=sqrt(64-x^2) on its domain.   Answer: 2pi   I know that the limits of integration is from -8 to 8 but how do I take the integral of sqrt(64-x^2) dx?   Please show... more
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03/24/14

Find the integral?
Find the integral of abs(x+1) dx from -3 to 2.    abs means absolute value.   Answer: 13/2   Please show all your work. 
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03/24/14

Find the integral?
Find the integral of abs(x) dx from -1 to 3.   abs means absolute value.   Answer: 5   Please show all your work.
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03/23/14

Find the area enclosed?
Find the area enclosed by the ellipse with parametric equations x=2 cos θ and y=3 sin θ.    Answer: 6pi   Please show all your work.
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03/23/14

Find the area bounded by?
Find the area bounded by y=e^x, y=2, and the y-axis.    Answer: 2 ln(2)-1   Please show all your work.
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03/23/14

Find the maximum value?
Find the maximum value of the function f(x)=xe^-x.    Answer: 1/e   Please show all your work. 
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03/23/14

Find the total area bounded?
Find the total area bounded by the cubic x=y^3-y and the line x=3y.    Answer: 8   Please show all your work. 
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03/22/14

Please answer this calculus question?
At time t, a particle moving in the xy-plane is at position (x(t), y(t)), where x(t) and y(t) are not explicitly given. For t≥0, dx/dt=4t+1 and dy/dt=sin(t^2). At time t=0, x(0)=0 and... more
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03/22/14

Can you answer this calculus question?
Let f(x)=sin(x^2)+cos x.    cos (x)=1-(x^2)/2!+(x^4)/4!-(x^6)/6!+...   sin(x^2)=x^2-(x^6)/3!+(x^10)/5!-(x^14)/7!+...   Use the series for cos (x) and the series for sin(x^2) to write the... more
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03/20/14

Find the integral?
Find the integral of 4/(x^2+4) dx. 
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03/19/14

Find the area of the region bounded?
Find the area of the region bounded by the parabola y^2=x and the line x+y=2.    Answer: 9/2   Please show all your work. 
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03/19/14

Find the area of the region bounded?
Find the area of the region bounded by the parabola y=x^2-3 and the line y=1.    Answer: 32/3   Please show all your work. 
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03/18/14

Find the integral?
Find the integral of (tan θ-1)^2 dθ.    Answer: tan θ+2*ln abs(cos θ)+C where abs means absolute value.   Please show all your work. 
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03/18/14

How much distance?
A particle starting at rest at t=0 moves along a line so that its acceleration at time t is 12t ft/sec^2. How much distance does the particle cover during the first 3 sec?    Answer: 54... more
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03/18/14

Find the acceleration?
Find the acceleration (in ft/sec^2) needed to bring a particle moving with a velocity of 75 ft/sec to a stop in 5 sec.    Answer: -15   Please show all your work.
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03/16/14

Find the integral?
Find the integral e^(2x)/(1+e^x) dx.    Answer: e^x-ln(1+e^x)+C    
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03/16/14

Find the integral?
Find the integral of (2x-1)/(sqrt(4x-4x^2)) dx.    Answer: (-1/2)*sqrt(4x-4x^2)+C    
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