Question

Find the limit. $$ \lim _{x \rightarrow 7} \frac{5 x}{\sqrt{x+2}} $$

Short answer

The limit of the function as x approaches 7 is \(\frac{35}{3}\)

Step-by-step solution

Substitution Step

Substitute x=7 into the function \(\frac{5x}{\sqrt{x+2}}\). This results in \(\frac{5\cdot7}{\sqrt{7+2}} = \frac{35}{\sqrt{9}} = \frac{35}{3}\)

Determination of the Limit

The limit of the function as x approaches 7 is thus \(\frac{35}{3}\). Since the direct substitution of x yielded a meaningful number as opposed to zero or infinity, there was no need to apply more advanced methods to find the limit.