Question

Please answer quickly I just need to confirm my answer

Answer 1

Given

`\lim_(x\to5)(x^3-125)/(x-5)`

Find

Estimate value of a limit

Step-by-step explanation

As we have

`\lim_(x\to5)(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)(x^3-5^3)/(x-5) \\ \lim_(x\to5)((x-5)(x^2+5^2+5x))/(x-5) \\ \lim_(x\to5)x^2+25^+5x \\ 5^2+25+5*5 \\ 25+25+25 \\ 75 \end{gathered}`

Final Answer

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