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calculus

This is very easy but i am struck with one

This is findind limit calculus one. This would be very easy but i never factor high degrees. can anyone show me how to factor it.

lim((x^5-32)/(x-2),x=2)

lim((x^5-2^5)/(x-2),x=2)

Solution

  • As John suggested in the comments above: when x-->2 we handle a limit of type 0/0. In order to calculate it we use the derivative of the numerator and a derivative of the denominator:

    f'(X^5-2^5) = 5x^4
----------    ----
f'(x-2)     = 1

    if we'll substitute x with 2 we'll get:

    5*2^4
----- = 80
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