- #1

Yankel

- 395

- 0

Hello all,

I am trying to solve a limit:

\[\lim_{x\rightarrow 0}\frac{sinh (x)}{x}\]

I found many suggestions online, from complex numbers to Taylor approximations.

Finally I found a reasonable solution, but one move there doesn't make sense to me.

I am attaching a picture:

View attachment 9401

I have marked in blue the move I can't understand. How does the minus from the exponent goes down before the half ?

And one more thing, at the final move, I know that the limit is 1, I know it as a rule, but why is this rule apply ? Thank you !

I am trying to solve a limit:

\[\lim_{x\rightarrow 0}\frac{sinh (x)}{x}\]

I found many suggestions online, from complex numbers to Taylor approximations.

Finally I found a reasonable solution, but one move there doesn't make sense to me.

I am attaching a picture:

View attachment 9401

I have marked in blue the move I can't understand. How does the minus from the exponent goes down before the half ?

And one more thing, at the final move, I know that the limit is 1, I know it as a rule, but why is this rule apply ? Thank you !