AP Calculus

Limits

100

lim_x->0 sin(x)/x =

1

200

lim_{x-> ∞} ln(x)/x2 =

0

300

lim_{x-> ∞} (3x3+4x2+7)/(5x2+6x3) =

1/2

Logs

100

Rewrite Log₁₅ 2*5

log₁₅2+log₁₅5

200

log₂2⁵

5

300

log_e1

0

Derivatives

100

What is the derivative of y =cot(3x)?

y'=-3csc²(x)

200

What is the derivative of y=sqrt(9x²+4)?

y'=(9x)/(sqrt(9x²+4)

300

What is the derivative of y= x-xln(x)?

y'=-ln(x)

Integrals

100

Find and simplify: ∫ sin(3x) dx

-cos(3x)/(3) +c

200

Find and simplify: (d/dx) ∫^4x₅ sqrt(t) dt

8sqrt(x)

300

Find and simplify ∫ ln(x)/x dx

ln(x)²/(2)+c

Misc.

100

Simplify: sqrt(36x² +18)

3sqrt(4x²+2)

200

The definite integral could be interpreted as the net area between the graph of a  _______ and the _______.

function; x-axis

300

Evaluate: cos(sin^-1(1/2))

sqrt(3)/2