Differentiation 1
Differentiation 2
Anti-differentiation
Theorems
Applications
100

Find the derivative of f(x)=10ln(2x)

What is 10/x?

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

Using the Fundamental Theorem of Calculus, what is∫abF(x)dx=?

What is F(b)-F(a)?

100

Determine the area of the region bounded by f(x)=xe^(x^2), y=x+1, x=2, and the y=axis.

What is 3.5092?

200

Find the derivative of -9.33cos(x).

What is 933sin(x)/100?

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 area under the curve f(x)=9.1sin(x) on the interval [0, 2pi].

What is 36.4?

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

Define the Mean Value Theorem.

What is a theorem that states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b]?

300

Find the volume for solid of revolution between the curves y=2.3x+1, y=0.1e, and x=2.5 around the x-axis.

What is 139.364?

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

What is the particular solution to the differential equation dy/dx=9x(3)/e with the initial condition y(0)=1?

What is y=(27x^2)/(2e)-(329.271)?

400
Solve for y=f(x) when f(3)=2. dy/dx=x2+3x/y2
What is (2/3x3+2x2-32).5?
400

Define the Extreme Value Theorem.

What is a theorem that guarantees both a maximum and minimum value for a function under such conditions: It states the following: If a function f(x) is continuous on a closed interval [ a, b], then f(x) has both a maximum and minimum value on [ a, b]?

400

Suppose an object’s velocity is given by v(t)=e^1.2t+sin(0.9t). Calculate the displacement of the object from t=1 to t=9.6.

What is 83923.678 units?

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 equation of the line tangent to f(x)=1.23x^1.5+2x at x=0.

What is y=2x?

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