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Question
`lim_("x" -> -2) sqrt ("x"^2 + 5 - 3)/("x" + 2)` is equal to ____________.
Options
`-2/3`
None of these
0
`2/3`
MCQ
Fill in the Blanks
Solution
`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`
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