Evaluate `lim_(x rarr 3) [(x^(5)-243)/(x^(2)-9)]`.

1.	Evaluate `lim_(x rarr 3) [(x^(5)-243)/(x^(2)-9)]`.
Answer» `underset(x rarr 3)("lim")[(x^(5)-243)/(x^(2)-9)]=underset(x rarr 3)("lim")[(x^(5)-3^(5))/(x^(2)-3^(2))]` `" "=(5)/(2)3^(5-2)" "(therefore underset(x rarr a)("lim")[(x^(m)-a^(m))/(x^(n)-a^(n))]=(m)/(n)a^(m-n))` `" "=(5)/(2)*3^(3)=(135)/(2)`.

Discussion

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