Question

`lim_("x" -> -3) sqrt("x"^2 + 7 - 4)/("x" + 3)` is equal to ____________.

Options

• `4/3`

• `-3/4`

• None of these

• `3/4`

Answer 1

`lim_("x" -> -3) sqrt("x"^2 + 7 - 4)/("x" + 3)` is equal to `underline(-3/4)`.

Explanation:

`lim_("x" -> -3) sqrt("x"^2 + 7 - 4)/("x" + 3)`

`=  lim_("x" -> -3) ("x"^2 + 7 - 16)/(("x" + 3)("x"^2 + 7 + 4))`

`=  lim_("x" -> -3)("x"^2 - 9)/(("x" + 3)(sqrt( "x"^2 + 7 + 4))`

`=  lim_("x" -> -3) ("x"- 3)/((sqrt("x"^2 + 7 + 4))`

`= (-3 -3)/((sqrt(9 + 7 + 4))`

`= - 3/4`