Calculus Test 1 Review Game

Limits

100

find limit at x=12

(24x)/x²

What is 2?

200

Find the limit of (x^2 - 6x +5) / (x - 5) as x goes to 5.

What is 4?

300

Find the limit as x approaches 1

1/(x-1)

What is does not exist?

400

lim (3-2x²)/(3x-1)
x→∞

What is -∞?

500

find limit at x=1

(x²)/(x-1)

What is does not exist?

Derivatives

100

d/dx 3x²-x+3 =

What is 6x-1?

200

d/dx 4x⁷-8x+3x⁴+12 = ?

What is 28x⁶+12x³-8?

300

d/dx x³lnx = ?

What is 3x²lnx + x²?

400

d/dx (x²-1)³/ x²+1 = ?

What is 4x(x²-1)?

500

d/dx x²sin³(5x) = ?

What is 2xsin³(5x) + 15x²sin²(5x)cos(5x) ?

Algebra

100

Find the domain of the function:

f(x) = (1/x+1) + 3

What is (-infinity, -1)U(-1, infinity)?

200

Is the function even, odd, or neither:

f(x) = x⁵+x

What is odd?

300

Simplify the following:

(y⁴(x³y^-2)² / 2x^-1

What is x⁷/2?

400

Turn into a single fraction:

2sqrt(t+3) + (1-2t)/(sqrt(t+3))

What is 7/sqrt(t+3)

500

Find (f o g) for the following functions:
f(x) = x² + 3x

g(x) = x + 4

What is x²+11x+28?

Definintions/Rules

100

The derivative calculates what?

The instantaneous slope/instantaneous velocity 

200

Defind the product rule using f(x)*g(x)

What is f'(x)g(x)+f(x)g'(x)?

300

Define the quotient rule using f(x)/g(x)

What is [f'(x)g(x) - f(x)g'(x)]/g(x)² ?

400

What are the three requirements for continuity?

1. f(c) must exist

2. the limit as x approaches c must exist

3. f(c) = the limit as x approaches c

500

What is the limit definition of a derivative?

Limit as h approaches 0 of:

[f(x+h) - f(x)] / h

Surprise!

100

When is your exam?

What is Friday September 20th?

200

Describe the rules for limits at infinity

When the degree of the numerator > degree of denominator: the limit is positive or negative infinity

When the degree of the numerator < degree of denominator: the limit is 0

When the degree of the numerator = degree of denominator: the limit is the coeffiencent of the numerator / the coeffiencent of the denominator

300

Find the equation of the tangent line at (1,4) for the following function:
f(x) = x⁴+6x+7

What is y = 10x-6?

400

d/dx (x³lnx)/(x+2) = ?

What is [(3x²lnx * (x+2)) - x³lnx]/(x+2)² ?

500

What are the four kinds of discontinuities? 

Jump: when the curve "breaks" at a place and starts in another

Point: when a curve has a "hole" in it 

Essential: when a curve has a vertical asymptote

Removeable: when you have a rational expression with common factors in the numerator and denominator