AP Calculus: Review and Limits

Factoring

100

Factor x² - x -2

(x+1)(x-2)

200

Factor x³ + 5x² + 4x

(x²+ x)(x+4) or 

(x+1)(x² + 4x) or 

(x)(x+1)(x+4)

300

Factor 2x² - 16x +30

2(x-3)(x-5) or

(2x - 6)(x - 5) or

(x - 3)(2x - 10)

400

Factor xy² - yx - 6x

x(y + 2)(y - 3)

500

Factor xh² - hkx + ghx - gkx

(x)(h+g)(h-k)

Logarithms

100

Log₂ 8 equals the following:

n = 3

200

Log₅ (1/25) equals the following:

n = -2

300

ln e⁵ equals the following

n = 5

400

Express ln(x(2x + 5)³)

ln x + 3ln(2x + 5)

500

Solve 2e^x+1 = 18 to the nearest thousandth.

x = 1.197

Operations on Functions

100

f(x) = x² - 4 and g(x) = x - 5 find

f(g(-1))

Equals 32

200

f(x) = x² - 4 and g(x) = x - 5 find

(f + g)(-3)

Equals -3

300

f(x) = x² - 4 and g(x) = x - 5 find

(fg)(2)

Equals 0

400

f(x) = x² - 4 and g(x) = x - 5 find

(g/f)(4)

Equals -(1/12)

500

f(x) = x² - 4 and g(x) = x - 5 find

(f/g)(5)

Is undefined

Limits

100

lim_x>0(x-5)(cos x) = 

-5

200

Rewrite lim_x>b (x³ - b³)/(x⁶ - b⁶) as

1/(2b³)

300

lim_x>0 (2 - sqrt(4-x))/x = 

1/4

400

lim_x>5 4 + log₂₅ 5x

5

500

lim_z>-1 (z³+1)/(z+1) = 

3