🎊🎉🪅Calc Review Jeopardy🪅🎉🎊

Integration by Substitution

100

∫(x³+1)²(3x²)dx

1/2x⁶+x³+C

200

∫√(2x+1)dx

1/3(2x+1)^2/3+C

300

∫e^5xdx

1/5e^5x+C

400

∫√(2x+1)dx from 0 to 4

26/3

500

∫dx/(x√lnx) from e to e⁴

2

Take the Derivative of Natural Log Functions

100

y=lnx dx

1/x

200

y=ln(4x)dx

1/x

300

y=ln√(3x+1)

3/(6x+2)

400

y=ln(x−2)−ln(x+2)

ln((x-2)/(x+2))

500

x²−3lny+y² =10

(2xy)/(3-2y²)

Take the Integral of Natural Log Functions

100

∫1/x(dx)

lnx+C

200

∫1/(4x)dx

(1/4)lnx + C

300

∫1/(3x+1)dx

1/3ln (3x+1) + C

400

∫(x²-2)/(x+1)dx, [0,2]

-ln3

500

Avg. value of f(x)=8/x², [2,4]

1

Inverse Functions

100

For a function to have an inverse, it must be?

1:1 function

200

A graphical test that can be used to determine if a function has an inverse is the what?

The horizontal line test

300

Find the inverse, f(x)=x²

f^-1(x)=√x

400

Find f^-1(7), f(x)=5-2x³

-1/6

500

True or False? If f is an even function, then f^-1 exists

False

Derivatives/Integrals of Exponential Functions

100

Solve, 50e^-x=30

x≈0.511

200

Find the derivative, y=e^5x

5e^5x

300

Find the derivative, y=(x+1)²e^x

e^x(x+1)(x+3)

400

Evaluate, ∫e^5x-3dx

(1/5)e^5x-3+C

500

∫e^-2xdx, [0,1]

(e²-1)/2e²