Question

For the graph e^(sinx) how many zeros are there on the closed interval {0,2pi}

Answer 1

0

Answer 2

\(e^{something} >0 \) for whatever the exponent is

Answer 3

There is at least one zero on this graph

Answer 4

how??

Answer 5

-1<sin <1

Answer 6

even when sin =0 , e^0 =1>0 no zero

Answer 7

when sin =-1 , \(e^{-1}=\dfrac{1}{e}>0\) still . No zero

Answer 8

The options are 1,2,3,or 4

Answer 9

If it is so, I am sorry. It is above my head.

Answer 10

Okay thank you anyway!

Answer 11

https://www.desmos.com/calculator/xwuw3tji5m

Answer 12

there has to be some kinda mistake...
like as @Loser66 says exp(sin(x)) is never zero
exp( ) function makes sure of that

i wonder if they meant the derivaitive's zero though they didn't say this

Answer 13

\[f(x)=e^{\sin(x)} \\ f'(x)=\cos(x)e^{\sin(x)} \\ \cos(x)e^{\sin(x)}=0 \\ \\\ \text{ here you would only need to solve } \cos(x)=0 \text{ on } [0,2\pi]\]

now again this is the zeros of your first derivative

exp(sin(x)) doesn't have any zeros itself