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 state?
What is there exists a point c in the interval (a,b) such that f'(c)=f(b)-f(a)/b-a, if a function is continuous on the closed interval [a,b] and differentiable on the open 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

6Find 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 is satisfied for f(x)=2x3+6x-2 on the interval [-2,2].

What is +- 2/(3).5?

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(0)=4. dy/dx=ycosx

What is f(x)=4esin(x)

400

Use the Fundamental Theorem of Calculus to find g'(x). g(x)=∫2x(9t+9)dt.

What is g'(x)=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 g'(x). g(x)=∫-3x(7t+9)dt.

What is g'(x)=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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