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Derivatives

100

What is the derivative of f(x)=5x³ ?

15x²

200

Find the derivative of f(x)=sin(x)cos(x)

cos²(x)-sin²(x)

300

If f(x)=ln(x²+1), find f’(x)

2x/x²+1

400

Find the derivative of f(x)=(x²+3)/(2x-1)

(2x²-2x-6)/(2x-1)²

500

If x²+y²=25, find dy/dx

-x/y

Curve Sketching

100

What does it mean when f’’(x)>0?

Concave up

200

How to find critical point of a function?

f’(x)=0

300

How to find inflection points of a graph?

f’’(x)=0

400

Describe the graph when f’(x)>0, f’’(x)<0

Increasing and concave down

500

Sketch a function with critical points at x=1,4;inflection point at x=2

Increasing until 1, decreasing until 4, concave change at 2

Limits

100

Find lim_x->2 x²-1

3

200

What is a removable discontinuity?

A hole in the graph and the limit exists but it’s undefined

300

Find lim_x->0 sinx/x

1

400

How to verity continuity

The limit on left and right side are equal

500

Find lim_x->0 1-cos x/x²

1/2

Volume by rotation

100

What method is used to rotate around the x-axis

Disk method

200

Formula for washer method

π∫_b^a [R²(x)-r²(x)]dx

300

volume of y=x^1/2 on [0,4] rotated about x-axis

Pi∫⁴₀ xdx=8pi

400

Formula of equilateral triangle

A = 3^-1/2/4 r²

500

Rotate between y=x and y=x² on [0,1] about x axis, find the volume

2pi/15

Integrals

100

What is ∫x dx

1/2 x²+C

200

What is Riemann Sum used for

To approximate the area under a curve

300

Evaluate ∫²₀ 3xdx

6

400

Area between y=x and y=x² from 0 to 1

1/6

500

Find ∫2x(x²+1)³dx

1/2 (x²+1)⁴ +C