Question

calculando lim x>5 (x3-125 / x-5) , qual o resultado?

Answer 1

Lim x -> 5 ( x³ -125 ) / (x-5 )

= ((x -5)* ( x² + 5x + 25)) / (x -5 ) ( corta o x - 5 com o x -5 )

= ( x² + 5x + 25) / 1 ( substitui pelo valor do limite )

Lim x -> 5 = 5 ² + 5*5 + 25 = 75

Answer 2

Resolução:

Aplique a regra de L`hôpital.

$\lim_{n \to \ 5}\frac{x^{3}-125}{x-5}\\ \\ \lim_{x \to \ 5} \frac{\frac{d}{dx}[x^{3}-125]}{\frac{d}{dx}[x-5]}\\ \\ \lim_{x \to \ 5}\frac{\frac{d}{dx}[x^{3}]+\frac{d}{dx}[-125]}{\frac{d}{dx}[x]+\frac{d}{dx}[-5]}\\ \\ \lim_{x \to \ 5} \frac{3x^{2}+0}{1+0}\\ \\ \lim_{x \to \ 5} \frac{3x^{2}}{1}\\ \\ 3.5^{2}\\ \\ 75$

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