Question

`lim_(y->0)e(1+ye^(-y/4))^(4/y) =` ?

Answer 1

`e^5`

Explanation:

`(e^x+4x)^(1/x)=e(1+4xe^(-x))^(1/x)` now making `y = 4x`

`lim_(y->0)e(1+ye^(-y/4))^(4/y) = e(lim_(y->0)(1+ye^(-y/4))^(1/y))^4=ecdot e^4= e^5`