Calculus BC

Derivatives

100

x

1

200

2x²

4x

300

5x³-8x+2

15x²-8

400

x^-2

-2x^-1

500

(2x+1)³

6(2x+1)²

Random

100

Lim x->-1 (2x)

-2

200

Lim x^2-3x-10/x^2-25 x->2

L=4/7

300

find f"(x) if f'(x)=12x³-12x+8

36x²-12

400

Find any points where the graph fails to be differentiable and explain why 3√(5x+7)

What is y is not differentiable at x=-7/5 due to a vertical tangent

500

Name the 4 types of Discontinuities

Hole, Jump, Infinity, Oscillating

Limits

100

Lim x->1 x

1

200

Lim x->3 (x-3)/(x²-9)

1/6

300

Lim x-> 2 (x²-4)

0

400

Lim x->∞ 3x/(x²-9)

0

500

Lim x->∞ 2x²/(x²+9)

2

AROC/IROC

100

Find the AROC of -x²-6x+5 at x=-1 and x=4

-9

200

Find the AROC of f(x) 4x-7 at x=-3 and x=5

4

300

Find the AROC of f(x) = 3x² at x=-2 and x=1

-3

400

Find the IROC of f(x) = x² at x=1

2

500

f(x)=x²

f(x+h)= (x+h)²

^{find the IROC of f'(x) = Lim h->0}

Lim h->0 2x = 0

Continuity

100

If f(x) = 5/x , is it continuous at x=0?

No!

200

F(X)= (5+4(x-2)²)/(x-2)

^{Is f(x) continuous at x=2}

no

300

is f(x) continuous at x=5?

f(x) = (x²-3x-10) / (x²-6x+5)

No!

400

What type of discontinuity is this function at x=2?

f(x) = (x²-5x+5) / (x²+2x-8)

Infinite

500

What type of discontinuity is the function at x=4?

f(x) = (x^2--10x+24) / (x²-5x+5)

Trick Question! It's continuous!