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Question
Select the correct answer from the given alternatives.
`lim_(x -> 5) ((sqrt(x + 4) - 3)/(sqrt(3x - 11) - 2))` =
Options
`(-2)/9`
`2/7`
`5/9`
`2/9`
Solution
`2/9`
Explanation;
`lim_(x -> 5) ((sqrt(x + 4) - 3)/(sqrt(3x - 11) - 2))`
= `lim_(x -> 5)[(sqrt(x + 4) - 3)/(sqrt(3x - 11) - 2) xx (sqrt(x + 4) + 3)/(sqrt(3x - 11) + 2) xx (sqrt(3x - 11) + 2)/(sqrt(x + 4) + 3)]`
= `lim_(x -> 5) ((x - 5) (sqrt(3x - 11) + 2))/((3x - 15)(sqrt(x + 4) + 3)`
= `lim_(x -> 5) (sqrt(3x - 11) + 2)/(3(sqrt(x + 4) + 3))`
= `(sqrt(4) + 2)/(3(sqrt(9) + 3)`
= `2/9`
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