Question

lim x->0 x⋅e^sin(x)/x

Calculate the limit.

Answer 1

Is it \[
e^{\frac{\sin(x)}x}
\]

Answer 2

Yup! :D

Answer 3

What is the limit of
\[
\lim_{x\to0}\frac{\sin(x)}x
\]

Answer 4

Are you asking me a different question or asking if this is my question?

Answer 5

That is part of your problem, so it is a different question that will help you decide about your limit

Answer 6

If the limit I asked you about is \(c\), then your limit will be \(e^c\)

Answer 7

http://www.cut-the-knot.org/arithmetic/algebra/ElementaryLimit.shtml

Answer 8

well, sin(x)/x is 1 right?

Answer 9

Yes, an elementary limit was the word I was looking for :)

Answer 10

So your original limit is \[ e^1=e\]

Answer 11

I´m sorry, but I´ll need more step by step help.... :P

Answer 12

\[
\lim_{x\to 0} \, e^{\frac{\sin (x)}{x}}=e^{\lim_{x\to 0} \, \frac{\sin (x)}{x}}=e^1=e

\]

Answer 13

But what happened to x in X⋅e^sin(x)/x?

Answer 14

`is it ` \(e^{\frac{\sin(x)}x}\) `?`
`yup! :D`.

Answer 15

With the factor x, the limit becomes 0\(\times\)e=?

Answer 16

so in the end we´ll have 0 x e^1? Is the limit 0?

Answer 17

Yes, with the multiplier x.

Answer 18

with the multiplier x? Doesn´t that make it automatically 0?

Answer 19

Not all the time.
Try
\(f(x)=x\times \frac{1}{(1-x)^2-1}\) as x-> 0