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Calc 1

100

The derivative of 5x²

What is 10x?

200

Evaluate lim_x->0  x/[3-sqrt(x+9)]

What is -6.

300

The derivative of sin(x)*x²

What is cos(x)*x²+2sin(x)*x?

400

Evaluate the indefinite integral of ∫(x²+2x+1)dx

x³/3+x²+x+C

500

The derivative of sin(2e^2x²)

What is 4x*2e^2x²*cos(2e^2x²)?

Calc 2

100

Evaluate the indefinite integral ∫sin(3x)dx

What is -(1/3)cos(3x)+C?

200

Evaluate the limit_x->0 (x-2)/(2x-4)

What is 1/2?

300

Evaluate the definite integral ₁∫²2xdx

What is 3?

400

Evaluate the improper integral ₀∫^∞ e^-xdx

What is 1?

500

Evaluate the indefinite integral ∫x²e^xdx

What is x²e^x-2xe^x+2e^x+C?

Calc 4

300

Evaluate the Partial derivatives of 

f(x, y, z) = 4xy+e^yz-16x²z³

f_x=4y-32xz³

f_y=4x+e^yz

f_z=e^y-48x²z²

400

Evaluate the derivative of z with respect to t (dz/dt) using the chain rule:

z=x²e^y

x=sin(t), y = ln(t)

What is dz/dt=2xe^y*(cos(t))+x²e^y*1/t?

500

Evaluate the triple integral 

₂∫³_-1∫⁴₁∫⁰ (4x²y-z⁴)dzdydx

What is -755/4?

Linear Analysis

300

evaluate the differential equation:

(1/y)*dy/dx=sin(x)

ln|y|=-cos(x)+C or y = Ce^-cos(x)

400

Evaluate the general solution for the differential equation 

y''(t)+4y'(t)+4y(t)=0

What is y(t) = C₁e^-2t+C₂te^-2t?

500

solve for y(t) given the following:

y'(t)+4y(t)=5e^t, y(0)=0

What is y(t)=e^t-e^-4t