Differentiation 1
Differentiation 2
Anti-differentiation
Theorems
Applications
100
Find the derivative of f(x)=3/2x2
What is 3x?
100
Find dy/dx. xy2+y3+x2=10
What is (-2x-y2)/(2xy+3y2)?
100
Integrate F'(x)=3x2+6x.
What is x3+3x2+C?
100
Complete the Fundamental Theorem of Calculus. ∫abF(x)dx=?
What is F(b)-F(a)?
100
Find the area of the region bounded by f(x)=x2-3x-10 and g(x)=-x2+5x+14.
What is 170.667?
200
Find the derivative of 7x3+9x2+5x
What is 21x2+18x+5?
200
Find the derivative of f(x)=ln(x3+3x2+7).
What is (3x2+6x)/(x3+3x2+7)?
200
Integrate F'(x) = x2
What is (x3/3 +C
200

What does the Mean Value Theorem for Integrals state?

There exists a point c in the interval (a,b) such that f(c)=(1/b-a)int_a^b f(x)dx, if a function is continuous on the closed interval [a,b].

200
Find the average acceleration of a particle over the interval (0,50) given v(50)=80ft/sec and an initial velocity of 10 ft/sec. Include units in your answer.
What is 7/5 ft/sec2?
300
Find the slope of f(x)=5/3x3-3x2-1/x2 at x=-1
What is 9?
300
Find dy/dx for the following function: x2y3+y2+3x=y.
What is (-3-2xy3)/(3x2y2+2y-1)?
300
Find the equation of F given F'(x)=x3-3x2+7x+8 and F(0)=5
What is F(x)=(x4/4)-x3+3.5x2+8x+5
300

Find a value c such that the conclusion of the mean value theorem for integrals is satisfied for f(x)=8-2x on the interval [0,4].

c=2

300
The rate of change of radius r of a circle is 4 cm/s. Find the rate of change of Area A when r=2cm.
What is 16π?
400
Find the derivative of f(x)=(x+3)3/(x-2)2-x2(7x+7)
What is (x+3)2[3(x-2)-2(x+3)]/(x-2)3-21x2-14x?
400
Find the derivative of f(x)=tan(3x).
What is 3sec2(3x)
400
Solve for y=f(x) when f(3)=2. dy/dx=x2+3x/y2
What is (2/3x3+2x2-32).5?
400
Use the second Fundamental Theorem of Calculus to find F'(x). F(x)=∫2x(9t+9)dt.
What is 9x+9?
400
The acceleration of a particle is given by the function a(t)=3t2+7. Find the position function of the particle given that its initial velocity is 10 m/sec and an initial height of 80m.
What is s(t)=(t4/4)+3.5t2+10t+80?
500
Find the derivative of f(x)=3x2+7x-2 using the limit process.
What is 6x+7?
500
Solve for d2y/dx2 when y2=3x2+4x+y at the point (2,5).
What is -.036?
500
Integrate x/(4+x2).5.
What is (4+x2).5+C?
500
Use the second Fundamental Theorem of Calculus to find F'(x). F(x)=∫-3x(7t+9)dt.
What is 7x+9?
500
Find the volume of the solid generated by revolving the region bounded by y=x2, the x-axis, and x=2 around the y-axis.
What is 8π?
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