Limit of e^(2x) / sinh(2x) as x approaches infinity

[ccha]

Homework Statement

Find the limit of e^(2x) / sinh(2x), as x approaches infinity.

Homework Equations

The Attempt at a Solution

Changed equation to e^(2x) / [(e^(2x) - e^(-2x)) / 2]. Based of the sinh identity.

found limit of e^(2x) = ∞ ... e^(-2x) = 0 ... 2 = 2 ...

New equation ( ∞ ) / [( ∞ - 0 ) / 2]

...

I am unsure how to continue after this.

 

[tiny-tim]

Welcome to PF!

Hi ccha ! Welcome to PF!

(try using the X² tag just above the Reply box )

… Changed equation to e^(2x) / [(e^(2x) - e^(-2x)) / 2]. Based of the sinh identity.

Now divide top and bottom by e^2x …

what do you get? ​