Question

please answer quickly I just need to confirm my answer

Answer 1

Given

$\lim_{x\to5}\frac{x^3-125}{x-5}$

Find

Estimate value of a limit

Explanation

As we have

$\lim_{x\to5}\frac{x^3-125}{x-5}$

we use formula to find limit

$a^3-b^3=(a-b)(a^2+b^2+ab)$

$\begin{gathered} \lim_{x\to5}\frac{x^3-5^3}{x-5} \\ \lim_{x\to5}\frac{(x-5)(x^2+5^2+5x)}{x-5} \\ \lim_{x\to5}x^2+25^+5x \\ 5^2+25+5\times5 \\ 25+25+25 \\ 75 \end{gathered}$

Final Answer

The estimate value of a limit is 75. So, the correct option is 3.