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Question
Select the correct answer from the given alternatives.
`lim_(x -> -2)((x^7 + 128)/(x^3 + 8))` =
Options
`56/3`
`112/3`
`121/3`
`28/3`
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Solution
`112/3`
Explanation;
`lim_(x -> -2)(x^7 + 128)/(x^3 + 8)`
= `(lim_(x -> -2) (x^7 - (- 2)^7)/(x - ( - 2)))/(lim_(x -> -2)(x^3 - ( - 2)^3)/(x - (- 2)))`
= `(7( - 2)^6)/(3(- 2)^2)`
= `112/3 ...[because lim_(x -> "a") (x^"n" - "a"^"n")/(x - "a") = "na"^("n" - 1)]`
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