How Does the Natural Exponential Function Influence Trigonometric Outcomes?

[cnc86666]

1. Let f(x)=sin(e^x)

a. Find 2 values of x satisfying f(x)=0

b. What is the range of f(x)

c. Find the value(s) of x that maximize f on [3.8,4] (use calculus)



2. y=e^x if and only if x=ln y



3.a. x=-infinity because the limit of e^x as x approaches -infinity is 0. and also, x=infinity because limit e^x as a approaches infinity=infinity

b.The range of f(x) is (0,infinity)

c. the values of x that maximize f on 3.81 and 3.95

 

[micromass]

It might be better in this format:

Homework Statement

Let f(x)=sin(e^x)

a. Find 2 values of x satisfying f(x)=0

b. What is the range of f(x)

c. Find the value(s) of x that maximize f on [3.8,4] (use calculus)

Homework Equations

y=e^x if and only if x=ln y

The Attempt at a Solution

a. x=-infinity because the limit of e^x as x approaches -infinity is 0. and also, x=infinity because limit e^x as a approaches infinity=infinity

b.The range of f(x) is (0,infinity)

c. the values of x that maximize f on 3.81 and 3.95[/QUOTE]

 

[HallsofIvy]

Thanks, micromass.

(a) "infiinity" and "-infinity" are NOT "values of x" so I doubt those are acceptable answers. sin(y)= 0 for y any multiple of $\pi$. You just need to find x such that $e^x= \pi$ and, say, $e^x= 2\pi$.

(b) Why does the range not include negative numbers? $sin(3\pi/2)= -1$ and there certainly exist x such that $e^x= 3\pi/2$. And how could $sin(e^x)$ be larger than 1?

(c) I get more than just two points.