Question

Evaluate the limit (lim(x --> 4) [(x^2 -2)/(3x - 2)]​

Answer 1

Step-by-step explanation:

The above photo of answer can hopely helpful to you.

Answer 2

Explanation:

$\red \bigstar \: \tt \large lim_{x \rightarrow4}( \dfrac{ {x}^{2} - 2 }{3x - 2} ) \\ \\ { \bold{ \underline{Applying \: L - Hospital \: rule,}}} \\ \\ \tt \leadsto \: lim_{x \rightarrow4}( \dfrac{ \dfrac{d}{dx}(x {}^{2} - 2) }{ \dfrac{d}{dx} (3x - 2)} \\ \\ \tt \leadsto \: lim_{x \rightarrow4}( \dfrac{ \dfrac{d}{dx}(x {}^{2} ) - \dfrac{d}{dx} (2)}{ \dfrac{d}{dx}(3x) - \dfrac{d}{dx} (2) } \\ \\ \tt \leadsto \: lim_{x \rightarrow4}( \frac{2x - 0}{3 - 0} ) \\ \\ \tt \leadsto \: lim_{x \rightarrow4}( \frac{2x}{3} ) \\ \\ \tt \leadsto \:( \frac{2 \times 4}{3} ) \\ \\ \tt \leadsto ( \frac{8}{3} ) \: \green \bigstar$

Hence,

$\bull\boxed{\tt \large lim_{x \rightarrow4}( \dfrac{ {x}^{2} - 2 }{3x - 2} ) = \dfrac{8}{3}}$

[ Note :- Refer to the attachment for important limits formulae. ]