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Question
Evaluate the following limits:
`lim_(x -> 2) (x^4 - 16)/(x - 2)`
Solution
`lim_(x -> 2) (x^4 - 16)/(x - 2) = lim_(x -> 2) ((x^2)^2 - 4^2)/(x - 2)`
= `lim_(x-> 2) ((x^2 - 4)(x^2 + 4))/(x - 2)`
= `lim_(x -> 2) ((x^2 - 2^2)(x^2 + ))/(x - 2)`
= `lim_(x -> 2)((x + 2)(x - 2)(x^2 + 4))/(x - 2)`
= `lim_(x -> 2) (x + 2)(x^2 + 4)`
= `(2 + 2)(2^2 + 4)`
= 4 × (4 + 4)
`lim_(x -> 2) (x^4 - 16)/(x - 2)` = 4 × 8
= 32
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