AP Calculus Review GAME!!

Limits

100

lim (x→−3) (x²-x-12)/(x+3)

What is -7

200

lim (h->0) ((2+h)² - 4)/ h 

What is 4

300

lim (t->9) (3- √t) / ( 9 - t)

What is 1/6

400

lim (w->2) (1/w - 1/2) /  (w-2)

What is -1/4

500

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

What is 1

Derivatives

100

Find the derivative of the function: g(x)= 3xsin²x 

What is 3sin²x + 6xsinxcosx

200

Find the derivative of the function: y= 5 secx

What is y'= 5 secxtanx

300

y= (2x² +5)⁷

What is y'=28x(2x² +5)⁶

400

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

What is f(x)= (-ln7*7^1/x)/ x²

500

Find the derivative of the function: y= (x²+cosx)/x⁵

What is y'= ( x(2x-sinx) - 5(x² + cosx) ) / x⁶

Derivatives Part 2

100

y= [(3x-2x³)(5+4x)] 

What is -24x²+4x+15

200

d/dx [5x³(sinx)]

What is 15x²(sinx)+5x³(cosx)

300

d/dx(3z²-4z)

What is 6z-4

400

d/dx (3t⁵ cost -2t⁹)

What is 15t⁴cost - 3t⁵sint - 18t⁸

500

f(x) = arsinx

what is 1/(1-x²)^1/2

Integrals

100

Integrate: ∫e^4x dx

What is 0.25e^4x + C

200

∫ sin x dx

What is -cosx +C

300

Integrate: ∫(5/x) dx

What is 5ln|x| + C

400

Integrate: ∫( √x+3) dx

What is 2x^3/2/3 + 3x +C

500

Integrate: ∫ sin x cos x dx

What is - cos²x / 2 +C

Antiderivatives

100

∫ 15x⁴ dx

What is 3x⁵+C

200

∫ -3x² dx

What is -x³ +c

300

∫ 2/z² dz

What is -1/z² +c

400

∫ cotx (sinx) dx

What is sinx+C

500

∫ (7t+8)³ dt

What is (7t+8)⁴/28 + C