Compute lim x- 2 1 x-2 - 4 x 2 -4

We have, #10; #10; x→ 2lim ( 1x 2 4x^2 4 #10;) #10; #10; ⇒x→ 2lim ( 1( #10;x 2 ) 4( x 2 )( x+2 )) #10; #10; ⇒x→ 2lim ( x+2 4( #1 ...

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Factorization Method Form to Remove Indeterminate Form

Compute lim...

Question

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

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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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