the great calculus journey by jesse governale, tom sawtelle, and jacob donald

The Great Calculus Journey

by Jesse Governale, Tom Sawtelle, and Jacob Donald

JEOPARDY BOARDLimits Graphing Limits

(algebraic) Derivatives Chapter 1 Calc Potpourri

$100 $100 $100 $100 $100 $100

$200 $200 $200 $200 $200 $200

$300 $300 $300 $300 $300 $300

$400 $400 $400 $400 $400 $400

$500 $500 $500 $500 $500 $500

FINAL JEOPARDY

Sketch the graph given the criteria:

Limits- $100 Question

Click to see answer

Note: Your answer is correct based on the placement of the given criteria, not the shape. You could use straight lines instead of the

parabolic curves shown in the example solution above.

Limits - $100 Answer

Click to return to Jeopardy Board

Show there is a zero of the function y=3x^2+2x-1 using the Intermediate

Value Theorem

Limits - $200 Question

Click to see answer

1. Function is a Polynomial , therefore it is continuous everywhere

2. F(0)= -1 F(1)=4

3. Therefore, by IVT there exists a value C such that F(C)=0



Using the precise Definition of a limit, prove=3

Limits- $300 Question

Click to see answer

Restriction: 3<x<50<d<3(Ɛ-3)



On what interval is the given equation

continuous?


Click to see answer

Polynomial, therefore it is continuous from (-∞,∞)



Find the slope of the tangent line to the curve

described below.

Hint: use


Click to see answer

= 6



The table shows (lifetime) peptic ulcer rates (per 100 population) for various family incomes as

reported by the National Health Interview Survey. Make a scatter plot of these data and decide

whether a linear model is appropriate.

Graphing - $100 Question

Click to see answer

A linear model is appropriate.Graphing - $100 Answer


Determine lim 1 / (x^3 - 1) x-->1 from the left

and lim 1 / (x^3 - 1) x-->1 from the right

from a graph of f


Click to see answer

lim 1 / (x^3 - 1) = - infinity

x-->1 from the left

lim 1 / (x^3 - 1) = infinity

x-->1 from the left

Graphing - $200 Answer


Explain why the function is discontinuous at the given number

a. Sketch the graph of the function.

f(x) = ln I x - 2 Ia = 2


Click to see answer

The function is discontinuous at a because ln(0) is undefined.



Use a graph of f(x)= (1 - 2/x)^x to estimate the value of limx→ infinity f(x)

to two decimal places


Click to see answer

y = .10Graphing - $400 Answer


Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the curve and

the tangent lines on the same screen.

y = 3x^2 - x^3 (1,2)


Click to see answer

(y - 2) = 3(x - 1)



Solve the limit using Algebra

Hint: Common Denominator

Limits (alg) - $100 Question

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Limits (alg) - $100 Answer


Solve the Limit using Algebra


Click to see answer


Hint: Conjugate


Click to see answer



Click to see answer

Limits (alg)- $500 Answer


What is the derivative ofx2+7x-18

Derivatives - $100 Question

Click to see answer

2x+7

Derivatives- $100 Answer


What is the derivative of4x2+17x+45

Derivatives - $200 Question

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8x+17

Derivatives - $200 Answer


solve for f(x)’’5x3+8x2-12x+42

Derivatives- $300 Question

Click to see answer

30x+16



Solve for f(x)’’f(x)=4x4-14x3-12x2+13x+19


Click to see answer

48x2-84x-24



Solve for f(x)’’’f(x)=4x5-6x4-3x3+4x2-7x+34


Click to see answer

240x2-144x-18



Where does does the graph move when y=f(x-

6)?

Chapter 1 - $100 Question

Click to see answer

6 units to the right

Chapter 1 - $100 Answer


Find sec(tan-112/5)

Chapter 1 - $200 Question

Click to see answer

13/5

Topic 5 - $200 Answer


What is log .0001Chapter 1- $300 Question

Click to see answer

-4

Chapter 1- $300 Answer


Find the line segment that connect points (-3,4) with (1,-2).

Chapter 1- $400 Question

Click to see answer

y=-3/2x+.5



What is f(g(h(4)))?Chapter 1- $500 Question

Click to see answer

1 2 3 4 5 6 7

f(x) 2 3 1 5 2 6 4

g(x) 6 1 3 6 4 5 4

h(x) 3 5 4 3 7 7 8

f(g(h(4))) = 1



Find the derivative of (e)^(e^x)

Calc Potpourri - $100 Question

Click to see answer

f’ = (e)^(e^x) * e^x

Calc Potpourri - $100 Answer


Name the four ways that you can represent a

function.


Click to see answer

Verbally, numerically, visually, and algebraicly



Which one is f(x) and f’(x)?


Click to see answer

Red = f’(x)Green = f(x)



Use a table of values to estimate the value of the

limit. lim [sqrt(x+4) - 2] / x x-->0


Click to see answer

lim = 0.250 x-->0



Find the derivative of y = cos(sqrt(sin(tan(pi*x)))


Click to see answer

f’ = -sin(sqrt(sin(tan(pi*x))) * (½)(sin(tan(pi*x)))^(-½) * cos(tan(pi*x)) * sec^2(x) * pi



Topic: Type topic here

FINAL

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Final Jeopardy Question

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Solve for y’


Final Jeopardy Answer

See yellow sticky inside envelope for alternate answer.

the great calculus journey by jesse governale, tom sawtelle, and jacob donald

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