Question

`lim_(x -> 0) ((2 + x)^5 - 2)/((2 + x)^3 - 2)` = ______.

पर्याय

• 0

• 1

• `20/3`

• `3/20`

Answer 1

`lim_(x -> 0) ((2 + x)^5 - 2)/((2 + x)^3 - 2)` = `20/3`.

Explanation:

Applying L-Hospital 's rule,

`lim_(x -> 0) ((2 + x)^5 - 2)/((2 + x)^3 - 2) =  lim_(x -> 0) (5(2 + x)^4)/(3(2 + x)^2)`

= `20/3`