Calc AB Review

Limits

100

State three rules to find limits

What is Difference rule, Quotient rule, Product rule, Power rule, 

200

Evaluate lim as x → -3 (6+4t)/(t^2 +1), if it exists. 

-3/5

300

Evaluate lim as x -> 8 (2x^2-17x+8/8-x)

-15

400

lim x -> 0    x/ 3 - square root of x + 9

-6

500

lim as x -> 0 x-sinx / x^3

1/6

Basic Derivatives

100

Differentiate: x^2

2x

200

Differentiate: 4x^7 - 9x^6 + 12x^2

28x^6 - 54x^5 + 24x

300

Differentiate: (3/4x)^4 + (2/7x)^1/2 + x

(3x)^3 + (2/14x)^-1/2+ 1

400

Find y′ (x^1/2 + 5)(x^2 - 5)

2x(x^1/2) + 10x + ((x)(x^1/2)) / 2 - 5 / 2(x^1/2)

500

Find y′ sin(x) / ln(x)

x(ln(x))(cos(x)) - sin(x) / x ln^2 x

Advanced Derivatives

100

Use the quotient rule to find f '(x). Simplify your answer. f(x)= (x^3) / (x^2)+1

((x^4)+(3x^2)) / ((x^2)+1)

200

Use the quotient rule to find f '(x). Simplify your answer. (4+x^2) / (4-x^2)

16x / (4 - x^2) ^3

300

Differentiate: ln(sin x^1/3)

cot x^1/3 / 3x^2/3

400

Differentiate: (sin^-3) (e^x)

e^x / (1 - e^2x)^1/2

500

Differentiate: (x^3)(e^2x)(cos(x))

((3x^2) + (2x^3))((e^2x))(cos(x)) - (x^3)(e^2x)(sin(x))

Integrals

100

∫ 5x^4-18x^2+7 dx

x^5-6x^3+7x + C

200

∫ 12x^7-x^2+3 dx

3/2x^8-1/3x^3+3x + C

300

The integral going from 0 - pi/2  7sin(x) - 2cos(x)dx

5

400

The integral from 0 to 2 e^x+ 1/x^2 + 1 dx

e^2 +inverse tan (2) -1

500

The integral from 0 to 4 f(t) dt where f (t) = (piecewise function) 2t t > 1     1-3t^2 t < equal to 1

15

MISC.

100

Name the three types of discontinuity learned so far in AB Calc

Hole, Jump, Infinity 

200

What was calculus made for?

Physics

300

A function becomes non differentiable when? 

There's a cusp, corner, discontinuity, or a vertical tangent line.

400

Who invented calculus?

Isaac Newton and Gottfried Leibniz.

500

What is Ms. Szymanski's favorite movie? 

Stand and Deliver