Question

`lim_{x→-5} (sin^-1(x + 5))/(x^2 + 5x)` is equal to ______ 

Options

• 0

• ∞ 

• `-1/5`

• 5

Answer 1

`lim_{x→-5} (sin^-1(x + 5))/(x^2 + 5x)` is equal to `underline(-1/5)`.

Explanation:

Applying L-Hospital's rule,

`lim_{x→-5} (sin^-1(x + 5))/(x^2 + 5x) = lim_{x→-5} ((1/sqrt(1 - (x + 5)^2)))/(2x + 5)`

= `1/(-10 + 5)`

= `-1/5`