Question

lim x tends to 5 then :-

Answer 1

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Answer 2

ANSWER :

$\sf\lim_{x \to \:5} \frac{ {x}^{4} - 625}{ {x}^{3} - 125}$

$\implies \sf \lim_{x \to \: 5} \frac{( {x}^{2} + 25)( {x}^{2} - 25) }{( x - 5)( {x}^{2} + 5x + {5}^{2}) }$

$\implies \sf \lim_{x \to \: 5} \frac{( {x}^{2} + 25)( {x} + 5) \cancel{(x - 5) }}{ \cancel{( x - 5)}( {x}^{2} + 5x + {5}^{2}) }$

Putting value of lim

$\sf \implies \frac{(25 + 25)(5 + 5)}{ {5}^{2} + 5 \times 5 + {5}^{2} }$

$\sf \implies \frac{500}{75}$