Differentiation
Limits
Integration
Applications of Differentiation
Applications of Integration
100
The derivative of ((3)-(2x)-(x^2))/((x^2-1))
What is 2/((x+1)^2), x!=1
100
Find the limit as x approaches -3 of (x^2+x-6)/(x^2-9)
What is 5/6
100

Find the integral of (1/x^3)dx

What is (-1/2x^2)+C

100
Find the critical values of f(x)=x^2*(x-3)
What is x=0,2
100
Find the area of the region of f(y)=y^2=1, g(y)=0, y=-1, y=2
What is 6
200
The derivative of y=cos(3x)
What is -3*sin(3x)
200
Find the limit as x approaches -4 of (x+3)^2
What is 1
200
Find the integral from 0 to 1 of ((2t-1)^2)dt
What is 1/3
200
Find the limit as x approaches infinity of x/(x^2-1)
What is 0
200
Find the arc length of y=2/3x^(3/2)+1 on the interval (0,1)
What is 1.219
300
The derivative of (x^3)*cos(x)
What is x^2(3cosx-xsinx)
300
Find the limit as x approaches 0+ of 2/sinx
What is infinity
300
Find the integral of (x)/((1-x^2)^3) dx
What is 1/(4(1-x^2)^2)+C
300
Find all relative extrema of f(x)=(x-5)^2
What is (5,0) is a relative minimun
300
Evaluate the integral of (x*cosx) dx
What is x*sinx + cosx + C
400
The derivative of y=2xsinx+x^2cosx
What is 4xcosx+(2-x^2)sinx
400
Find the vertical asymptotes of and holes of (x^2-2x-15)/(x^3-5x^2+x-5)
What is no vertical asymptotes and a hole at x=5
400
Find the integral of cot^2(x) dx
What is -cotx-x+C
400
Find all relative extrema of f(x)=x+(4/x)
What is (2,4) is a relative minimum and (-2,-4) is a relative maximum
400
Evaluate the intergral of (lnx^2)/(x)
What is (lnx)^2 + C
500
The derivative of y=sin(xy)
What is (ycos(xy))/(1-xcos(xy))
500
Find the limit as x approaches 0 of (1-cosx)/(sinx)
What is 0
500
Find the integral of (x(1-3x^2)^4) dx
What is 1/30*((3x^2)-1)^5+C
500
Find the critical values of f(x)=sin^2(x)+cosx on the interval of 0
What is x=pi/3, pi, (5*pi)/3
500

Use the shell method to find the volume of the solid generated by revolving the plane about the line x=5 of y=4x-x^2, y=0

What is 64*pi

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