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

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.