Question

lim x³-1/x-1, solve in factorisation calculus methods
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Answer 1

Answer:

lim (x^3-1)/(x-1), x-->1

First we try to solve the function by substituting x with 1.

then, lim (1^3 - 1)/(1-1)= 0/0

0/0 means that this method has failed because 1 is a root for both upper and lower functions,

Now we will try to factorize the function to eliminate the common factor

lim (x^3 - 1)/(x-1) = lim (x-1)(x^2+x+1)/(x-1)

lim (x^2+x+1).

Now we substitute with 1

==> lim (x^2 +x+1) , x-->1  = lim(1^1+1+1) = 3

==> lim (x^3-1)/(x-1) = 3    when x-->1