Differential and Integral Calculus by Feliciano and Uy: Limit of a Function, Exercise 1.2, Problem 7

Evaluate \lim\limits_{x\to 3}\left(\frac{\sqrt{3x}}{x\sqrt{x+1}}\right).

SOLUTION:

Plug in the value x=3.

\lim\limits_{x\to 3}\left(\frac{\sqrt{3x}}{x\sqrt{x+1}}\right)=\frac{\sqrt{3\left(3\right)}}{3\sqrt{3+1}}

=\frac{\sqrt{9}}{3\sqrt{4}}

=\frac{3}{3\cdot 2}

=\frac{3}{6}

=\frac{1}{2}

 

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