Solve- lim x- 2 x 2 -4 - 3x-2 - x-2

Let L=lim _ x→ 2 x ^ 2 4 √( 3x 2 ) √( x+2 ) #160; #160; L=lim _ x→ 2 x ^ 2 4 [ ( 3x 2 ) ( x+2 ) #160; ] #160; #160; ×( √( 3x 2 ) +√( ...

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Theorems for Continuity

Solve: lim x...

Question

Solve:
$lim x \to 2 \frac{x^{2} - 4}{\sqrt{3 x - 2} - \sqrt{x + 2}}$

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lim x \to 2 \frac{x^{2} - 4}{\sqrt{x + 2} - \sqrt{3 x - 2}}

\begin{matrix} {lim}_{x \to 1} \frac{x^{2} - 3 x + 2}{x^{2} - 4 x + 3} {lim}_{x \to 2} \frac{x^{3} + x^{2} - 12}{x^{3} - x^{2} - x - 2} {lim}_{x \to \sqrt{2}} \frac{x^{2} + x \sqrt{2} - 4}{x^{2} - 3 x \sqrt{2} + 4} {lim}_{x \to 3} \frac{x^{3} - 3 x^{2} - x + 3}{x^{3} - 6 x^{2} + 9 x} \end{matrix}

lim x \to 1 [\frac{3}{x^{2} + x - 2} - \frac{4}{x^{2} + 2 x - 3}]

{lim}_{x \to 2} \frac{\sqrt{x^{3} - 4} - 2}{\sqrt{20 - x^{2}} - 4}

Evaluate the following one sided limits:

$(i) {lim}_{x \to 2^{+}} \frac{x - 3}{x^{2} - 4}$

$(i i) {lim}_{x \to 2^{-}} \frac{x - 3}{x^{2} - 4}$

$(i i i) {lim}_{x \to 0^{+}} \frac{1}{3 x}$

$(i v) {lim}_{x \to 8^{+}} \frac{2 x}{x + 8}$

$(v) {lim}_{x \to 0^{+}} \frac{2}{x^{\frac{1}{5}}}$

$(v i) {lim}_{x \to \frac{π^{-}}{2}} t a n x$

$(v i i) {lim}_{x \to \frac{π}{2^{+}}} s e c x$

$(v i i i) {lim}_{x \to 0^{-}} \frac{x^{2} - 3 x + 2}{x^{3} - 2 x^{2}}$

$(i x) {lim}_{x \to - 2^{+}} \frac{x^{2} - 1}{2 x + 4}$

$(x) {lim}_{x \to 0^{+}} (2 - c o t x)$

$(x i) {lim}_{x \to 0^{-}} 1 + c o s e c x$

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