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# If $\lim\limits_{x\to k}\large\frac{x^k-5^k}{x-5}$$=500 then positive value of k is (a)\;3\qquad(b)\;4\qquad(c)\;5\qquad(d)\;6 Can you answer this question? ## 1 Answer 0 votes \lim\limits_{x\to k}\large\frac{x^k-5^k}{x-5}$$=500$
$\Rightarrow k(5)^{k-1}=500$
$\Rightarrow k.5^{k-1}=4\times 5^{4-1}$
$\Rightarrow k=4$
Hence (b) is the correct option.
answered Dec 30, 2013