Question
Evaluate the following limits:

Given that $7 \mathrm{x} \leq \mathrm{f}(\mathrm{x}) \leq 3 \mathrm{x}^2-6$ for all $x$. Determine the value of $\lim _{x \rightarrow 3} f(x)$

Answer

$
\begin{array}{ll}
& 7 x \leq \mathrm{f}(x) \leq 3 x^2-6 \\
& \text { Taking limits as } x \rightarrow 3 \\
& \lim _{x \rightarrow 3}(7 x) \leq \lim _{x \rightarrow 3} \mathrm{f}(x) \leq \lim _{x \rightarrow 3}\left(3 x^2-6\right) \\
\therefore \quad & 7(3) \leq \lim _{x \rightarrow 3} \mathrm{f}(x) \leq 3(3)^2-6 \\
\therefore \quad & 21 \leq \lim _{x \rightarrow 3} \mathrm{f}(x) \leq 21 \\
&
\end{array}
$
Using squeeze theorem,
$
\lim _{x \rightarrow 3} f(x)=21
$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free