Calculus 1 Review Jeopardy

Limits

100

There is no b for which limx→c f(x) = b

What is the limit does not exist

200

f(x) = {x^3-4 for x<2 {2x for x>=2 What is the limit as x approaches 2 for f(x)?

both the limit from the right and the left equal 4 so the limit exists and is equal to 4

300

Name 3 of the rules to find limits

What is Difference Rule, Constant Multiple Rule, Product Rule, Power Rule, Quotient Rule

400

Name the 4 types of Discountinuties

What is Hole, Jump, Infinity, Oscillating

500

Answer the following Limit Question: Lim sinx/x as x approaches 0

1

Derivatives

100

If h(x) = 2x^2 + 1, find the slope of the tangent line at the point P(1, 3).

4

200

Find the derivative of y = 5x3 - √2x2 + 6x

15x2 - 2√2x + 6.

300

What is the general formula for derivatives?

lim f(x+h)−f(x)/h as h approaches 0

400

find the derivative of y=√13x^2-5x+8)

(26x-5)/(2√13x^2-5x+8)

500

Determine all the numbers c which satisfy the conclusions of the Mean Value Theorem for the following function. f(x)=x^3+2x^2-x on [-1,2]

c= 0.7863

Integrals

100

find ∫5dx from 0 to 4

20

200

Evaluate the following. pi ∫ (sin x+2)dx 0

2pi + 2

400

This equation's derivative is: 25x^3 - 12x^2 + X. Find its intergral

What is the derivative of 25x^4/4 - 4x^3 + x^2/2?

500

Integrate ∫(-1)^(3) ((2x+1)^2)dx.

57 1/3

Volume/Area

100

Method of which the shape of a circle with a hole in it to help us find the volume of a shape created by rotating two functions around an axis.

washer method

200

This formula is used to find areas with more than one curve.

What is ∫a^b(f(x)-g(x) )dx

300

Find the integral ∫5x^2+3dx from 0 to 4

118.667

400

Approximate the area under the curve f (x)=x^2+2, -2≤x≤ 1 with a Riemann sum, using six sub-intervals and right endpoints.

8.375

500

Find the volume of the solid rotated about the line y= -2 for the region bounded by y=√ x+2) and y=e^2

19.724