Question

`lim_("x" -> -2) sqrt ("x"^2 + 5 - 3)/("x" + 2)` is equal to ____________.

विकल्प

• `-2/3`

• None of these

• 0

• `2/3`

Answer 1

`lim_("x" -> -2) sqrt ("x"^2 + 5 - 3)/("x" + 2)` is equal to `underline(-2/3)`.

Explanation:

`lim_("x" -> -2) sqrt ("x"^2 + 5 - 3)/("x" + 2)`

`= lim_("x" -> -2) ("x"^2 + 5 - 9)/(("x" + 2)("x"^2 + 5 + 3))`

`= lim_("x" -> -2) ("x" - 2)/(sqrt("x"^2 + 5 + 3)`

`= -4/(3 + 3) = -2/3`