AP Calculus Review

Limits

100

lim x→−3 x^2-x-12/x+3

What is -7

200

lim (2+h)^2 - 4/ h h->0

What is 4

300

lim 3- √t/ t->9 9 - t

What is 1/6

400

lim 1/w - 1/2 / w->2 w-2

What is -1/4

500

lim cos [3pi/2 + x]- cos[3pi/2] / x->0 x

What is 1

Derivatives

100

Find the derivative of the function: g(x)= 3xsin^2x - x^2 cos x

What is x^1/2 (4-3x) /2(x^2 - 4x)^2

200

Find the derivative of the function: y= 5 secxtanx

What is y'= 5 secx (2tan^2x+1) or y'= 5 secx (tan^2x +sec^2x)

300

y= (2x^2 +5) ^7

What is y'=28x(2x^2 +5)^6

400

Find the derivative of the function: f(x)= 7 ^ 1/x

What is f(x)= -ln7*7^1/x / x^2

500

Find the derivative of the function: y= arccos [x/3]

What is y'= -√9-x^2

Derivatives Part 2

100

d [(3x-2x^3)(5+4x)] -- dx

What is -24x^2+4x+15

200

d/dx [5x^3-sinx]

What is 15x(sinx)+5x^3(cosx)

300

d/dx(3z^2-4z)

What us 6z-4

400

d/dx (3t^5 cost -2t^9)

What is 15t^4 - 3t^5sint-18t^8

500

Is f(x)= { |x-2| for x<2 (x-3)^2-1 for x=> 2

what is no because the values don't exist at the same points

Integrals

100

Integrate: ∫xe^x dx

What is xe^x - e^x + C

200

∫ x sin x dx

What is -xcosx + sinx +C

300

Integrate: ∫lnx dx

What is x ln x - x + C

400

Integrate: ∫x( √x+3) dx

What is (2/3)x(x+3)^3/2-(4/15)(x+3)^5/2+C

500

Integrate: ∫ x sin x cos x dx

What is (1/2)xsin^2x-(1/4)x +(1/8)sn 2x +C

Antiderivatives

100

∫ 15x^4 dx

What is 3x^5+C

200

∫ -3x^2 dx

What is -x^3 +c

300

∫ 2/z^2 dz

What is -1/z^2 +c

400

∫ cotx (sinx) dx

What is sinx+C

500

∫ (7t+8)^3 dt

What is (7t+8)^4 ----------- + C 28