Question 1What does MOOC stand for?Your AnswerScoreExplanation

Massive open online courseCorrect1.00

The sound a cow makes when it has the hiccups

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I just needed a place-holder quiz question so that the question numbers correspond to the section labels in the week 1 slide deck.Question 2Suppose an investor buys a perpetual annuity that pays $674.16 annually but agrees to let the seller skip the first two payments. How much should he pay if the interest rate is 6%? (Answer should be provided as a numerical answer)Answer for Question 2You entered:PreviewHelpYour AnswerScoreExplanation

11236-1236Correct1.00

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Calculate the value of a perpetual annuity that pays $674.16 annually then subtract the value of an annuity that makes two annual payments of $674.16.Question 3Which of the following statements is not a definition of a limit?Your AnswerScoreExplanation

The limit ofg(x)asxaexists, is finite, and equal tolif and only if for any>0, there is>0such that|g(x)l|.Correct1.00

The limit ofg(x)asxaexists, is finite, and equal tolif and only if for any>0, there is>0such that|g(x)l|0, there is>0such that|g(x)l|.

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Question 4Letf(x)=x21x1. Compute the limit off(x)asx1by factoring the numerator. (Answer should be provided as a numerical answer)Answer for Question 4You entered:PreviewHelpYour AnswerScoreExplanation

2Correct1.00

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Factor the numeratorx21=(x+1)(x1).Question 5The functionf(x)=x21x2+1is continuous for all real values of x.Your AnswerScoreExplanation

TrueCorrect1.00

False

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Polynomials are continuous everywhere and rational functions are continuous as long as the denominator is not equal to zero.Question 6Use the definition of the derivative to compute the derivative of the functionf(x)=x21.Answer for Question 6You entered:PreviewHelpYour AnswerScoreExplanation

2*xCorrect1.00

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Question 7Compute the derivative of the functionf(x)=x2sin(x2).Answer for Question 7You entered:PreviewHelpYour AnswerScoreExplanation

2*x*(sin(x^2)+(cos(x^2)*(x^2)))Correct1.00

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Think offas the product ofx2andsin(x2)and use the product rule. Don't forget to use the chain rule when computing the derivative ofsin(x2).Question 8The functionf(x)=x32x2has a critical point atx=43. Is it a minimum or a maximum?Your AnswerScoreExplanation

MinimumCorrect1.00

Maximum

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Compute the second derivative offand evaluate it at the critical pointx=43.Question 9Which of the following statements is incorrect?Your AnswerScoreExplanation

Duration can be negative.Correct1.00

Duration measures interest rate sensitivity.

The units of duration is years.

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Duration is a weighted average of future times so it can not be negative.Question 10Letf(x)=x21x1. Use lHopitals rule to compute the limit off(x)asx1. (Answer should be provided as a numerical answer)Answer for Question 10You entered:PreviewHelpYour AnswerScoreExplanation

2Correct1.00

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Sincelimx1g(x)=limx1x21=0andlimx1h(x)=limx1x1=0,limx1f(x)=limx1g(x)h(x)=limx1g(x)h(x).