Calculus Jeopardy (Tyler & Oliver)

Derivatives

100

Solve for the Derivative:

y = x³ - x² + x - 1

3x² - 2x + 1

200

Solve for the Derivative:

y = ln(x)

1/x

300

Solve for the Derivative:

y = (e^x)(sinx)

(e^x)(sinx) + (e^x)(cosx)

400

Solve for the Derivative:

y = -2(1 + x)⁴

-8(1 + x)²

500

Solve for the Derivative:

y = (2x² + 5x + 1)³

3(2x² + 5x + 1)²(4x + 5)

Integrals

100

Evaluate:

∫ [3x² + 5] dx

x³ + 5x + C

200

Evaluate:

∫ [4cos(3x)] dx

4/3 sin(3x) + c

300

Evaluate:

∫ [(du)/(a² + u²]

(1/a)arctan(u/a) + c

400

Evaluate on the interval [0,4]:

∫ [3x4 - 3x²] dx

2752/5

500

Evaluate (u-sub):

∫ [x(x+3)^1/2] dx

(2u^5/2/5) - (2u^3/2) + c

Limits & Continuity

100

Find the Limit:

    limx→5   x² + 1

26

200

Find the limit:

      limx→-3   (x² + x - 6)/(x + 3)

-5

300

Find the Limit:

limx→1   (((x + 1)^1/2) - 1)/(x)

 

1/2

400

Find the Limit (L'Hopital's Rule):

    limx→2   (x³ + 7x² + 10x)/(x² + x -6)

-6/5

500

Find the Limit:

    limx→-2   (x³ + 8)/(x² - 4)

-3

Random

100

If a particle's velocity is negative with a positive acceleration, is the particles speed increasing or decreasing?

decreasing

200

What are the critical values?

f(x) = x² + 4x + 5

-2

300

Find the linear approximation of f(x) = 2x² + 3x + 4 at x = -2. Use the linearization to approximate f(-1.9)

5.5

400

Write an equation to find the area between the curves.

Curve 1: y =1

Curve 2: y =cos²x

A = ∫ [(1 - cos²x)] dx

(integral from 0 to π)

500

We have 45m² of material to build a box with a square base and no top. Determine the dimensions that maximize the volume.

(Calculator)

length = width = 3.873

height = 1.9365