Calculus Review Game Part 1

Derivative

100

Find the derivative of f(x) = 4x³ + 8x² + 3x + 2

f'(x) = 12x² + 16x + 3

200

d/dx 4x⁵ − 5x⁴ 

20x⁴-20x³

300

Find the derivative of f(x) = - 1/2 x⁵

f'(x) = −5/2 x⁴

400

Find the derivative of f(x) = √x³ 

f′(x)=3/2x^1/2 or 3/2 √x

500

d/dx= x⁸+12x⁶-4x³+10x²-16x+4

f'(x)=8x⁷+72x⁵-12x²+20x-16

Limits

100

lim x->0 [(4+x)² -16]/x

8

200

lim x->3  (5x² - 8x -13) / (x² - 5)

2

300

lim x->-8     (7 + 8x + x^4/3)

-41

400

lim x->0  [(2+x)³ -8]/x

12

500

lim x-> 4  (2x²-12x+16)/(x²-x-12)

4/7

Area between curves

100

y = x² and y=x+2 [-1,2]

9/2

200

y = -x² + 9 and y = 0 [-3,3]

36

300

y = x² + 7 and y = 1/3x + 18

48

400

y = 3x, y = 3/5x, y = 28 - x²  [0,5]

30

500

y = √x and y=x² [0,1]

1/3