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Quiz 1: There is one question for each of the 10 topics from week 1. The time limit is 1 hour and you only get one try so make sure you have your notes and the week 1 slides handy. Good luck!

In accordance with the Coursera Honor Code, I (Anonymous Student) certify that the answers here are my own work.

Question 1

What does MOOC stand for?

Massive open online course

The sound a cow makes when it has the hiccups

Question 2

Suppose 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)

Help

Question 3

Which of the following statements is not a definition of a limit?

The limit of

g(x) $g(x)$ as

x→a $x \rightarrow a$ exists, is finite, and equal to

l $l$ if and only if for any

ϵ>0 $\epsilon \gt 0$ , there is

δ>0 $\delta \gt 0$ such that

|g(x)−l|<ϵ $|g(x) - l| \lt \epsilon$ for all

x>δ $x \gt \delta$ .

The limit of

g(x) $g(x)$ as

x→a $x \rightarrow a$ exists, is finite, and equal to

l $l$ if and only if for any

ϵ>0 $\epsilon \gt 0$ , there is

δ>0 $\delta \gt 0$ such that

|g(x)−l|<ϵ $|g(x) - l| \lt \epsilon$ for all

x $x$ in

(a−δ,a+δ) $(a - \delta, a + \delta)$ .

The limit of

g(x) $g(x)$ as

x→∞ $x \rightarrow \infty$ exists, is finite, and equal to

l $l$ if and only if for any

ϵ>0 $\epsilon \gt 0$ , there is

δ>0 $\delta \gt 0$ such that

|g(x)−l|<ϵ $|g(x) - l| \lt \epsilon$ for all

x>δ $x \gt \delta$ .

Question 4

Let

f(x)=x2−1x−1 $\displaystyle f(x) = \frac{x^2 - 1}{x - 1}$ . Compute the limit of

f(x) $f(x)$ as

x→1 $x \rightarrow 1$ by factoring the numerator. (Answer should be provided as a numerical answer)

Help

Question 5

The function

f(x)=x2−1x2+1 $\displaystyle f(x) = \frac{x^2 - 1}{x^2 + 1}$ is continuous for all real values of x.

True

False

Question 6

Use the definition of the derivative to compute the derivative of the function

f(x)=x2−1 $f(x) = x^2 - 1$ .

Help

Question 7

Compute the derivative of the function

f(x)=x2sin(x2) $f(x) = x^2 sin(x^2)$ .

Help

Question 8

The function

f(x)=x3−2x2 $f(x) = x^3 - 2x^2$ has a critical point at

x=43 $x = \frac{4}{3}$ . Is it a minimum or a maximum?

Minimum

Maximum

Question 9

Which of the following statements is incorrect?

The units of duration is years.

Duration can be negative.

Duration measures interest rate sensitivity.

Question 10

Let

f(x)=x2−1x−1 $\displaystyle f(x) = \frac{x^2 - 1}{x - 1}$ . Use l’Hoˆpital’s rule to compute the limit of

f(x) $f(x)$ as

x→1 $x \rightarrow 1$ . (Answer should be provided as a numerical answer)

Help

In accordance with the Coursera Honor Code, I (Anonymous Student) certify that the answers here are my own work.

You cannot submit your work until you agree to the Honor Code. Thanks!

Mathematical Methods for Quantitative Finance

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Mathematical Methods for Quantitative Financeby Dr. Kjell Konis

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