Resolved: "Find the following limits or state that they..."

Ayaana Buck

Answered question

2021-02-25

Find the following limits or state that they do not exist.

lim_{x \to 4} \frac{31 x - 42 \cdot \sqrt{x + 5}}{3 - \sqrt{x + 5}}

berggansS

Skilled2021-02-26Added 91 answers

Consider the provide expression,

lim_{x \to 4} \frac{31 x - 42 \cdot \sqrt{x + 5}}{3 - \sqrt{x + 5}}

Now, find the limit of the provided expression.

lim_{x \to 4} \frac{31 x - 42 \cdot \sqrt{x + 5}}{3 - \sqrt{x + 5}}

Its is not determinant form because the expression from is

\frac{0}{0}

Apply the L Hospital rule,

lim_{x \to 4} \frac{31 x - 42 \cdot \sqrt{x + 5}}{(3 - \sqrt{x + 5}} = lim_{x \to 4} \frac{31 - 42}{(2 \sqrt{x + 5})} (3 - \frac{1}{\sqrt{x + 5}})

So, it is a determinant form

lim_{x \to 4} \frac{31 x - 42 \cdot \sqrt{x + 5}}{3 - \sqrt{x + 5}} = lim_{x \to 4} \frac{31 - \frac{42}{2 \cdot \sqrt{x + 5}}}{3 - \frac{1}{\sqrt{x + 5}}}

= \frac{31 - \frac{42}{6}}{3 - \frac{1}{3}}

= \frac{24 \cdot 3}{8}

= 9

Hence, the limit is 9

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