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Evaluate the following limit: limx→2[x-3-2-3x-2] - Mathematics and Statistics

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Question

Evaluate the following limit:

`lim_(x -> 2)[(x^(-3) - 2^(-3))/(x - 2)]`

Evaluate
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Solution

`lim_(x -> 2)[(x^(-3) - 2^(-3))/(x - 2)]`

= (– 3) . (2)–4             ...`[because  lim_(x -> "a") (x^"n" - "a"^"n")/(x - "a") = "na"^("n" - 1)]`

= `-3xx1/2^4`

= `-3/16`

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Chapter 7: Limits - Exercise 7.1 [Page 139]

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