CPM Homework Help : CALC Problem 11-36

Multiple Choice: The graph of $f ( x ) = 1 + x + \frac { x ^ { 2 } } { 2 ! } + \frac { x ^ { 3 } } { 3 ! } + \frac { x ^ { 4 } } { 4 ! } +...$ best approximates which function near $x = 0$ ?

$f(x) = x^2$

$f(x) = e^x$

$f(x) =\operatorname{sin}x$

$f(x) =\operatorname{cos}x$

Hint:

$f(0) = 1$
Which choices match this situation?

$f^\prime(0) = 1$
Which choice matches this situation?