Find the following limit- limx - 1 - x3 - 4x-x3 - 8 -1 - x - -2x-x - 2 - -2-x - -2 -1 -

lim_x→ 1(x(x 2)(x+2)(x 2)(x^2+4x+4))^ 1 (√(x)(√(x)+√(2))(√(x) √(2))(√(x)+√(2)) √(2)√(x) √(2))^ 1 =lim_x→ 1(x(x+2)x^2+4x+4)^ 1 1 =lim_x→ 1(xx+2)^ ...

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Algebra of Limits

Find the foll...

Question

Find the following limit:
$lim x \to 1 ⎡ ⎣ {(\frac{x^{3} - 4 x}{x^{3} - 8})}^{- 1} - {(\frac{x + \sqrt{2 x}}{x - 2} - \frac{\sqrt{2}}{\sqrt{x} - \sqrt{2}})}^{- 1} ⎤ ⎦$

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Evaluate the following one sided limits:

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

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

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

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

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

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

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

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

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

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

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

lim x \to 9 (\frac{3 - \sqrt{x}}{9 - x} + \frac{1}{3 - \sqrt{x}} - 6. \frac{x^{2} + 162}{729 - x^{3}}) .

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