Consider the Two Functions $f ( x ) = e ^ { \sin x }$

question 90

Essay

Consider the two functions $f ( x ) = e ^ { \sin x }$ and $g ( x ) = \sin \left( e ^ { x } \right)$ (a) Which, if either, of these functions is periodic? Justify your answer.(b) For each function, consider the limit as x increases without bound. Does either function also increase without bound like an exponential function? Explain.(c) Where, if anywhere, does each function have an x-intercept? Justify your answer.(d) Where, if anywhere, does each function have a horizontal tangent line? Justify your answer.(e) Where, if anywhere, does each function attain its maximum value? its minimum value? Justify your answers.

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Definitions:

Extra Payments

Payments made on a loan that exceed the minimum required payment, often used to reduce the loan balance more quickly.

Compounded Monthly

A method of calculating interest in which the accrued interest is added to the principal sum every month, so that each subsequent interest calculation is based on a slightly higher amount.

Lifetime Interest

The total amount of interest that will be paid or earned over the entire life of a loan or investment.

Loan

A quantity of money that is lent and is supposed to be repaid along with an additional amount as interest.