Evaluate- lim x- 1 1 x 2 -x-2 - x x 3 -1

lim_x→11x^2+x 2 xx^3 1=lim_x→ 11(x 1)(x+2) x(x 1)(x^2+x+1) =lim_x→1x^2+x+1 x(x+2)(x 1)(x^2+x+1)(x+2)=lim_x→1x^2+x+1 x^2 2x(x 1)(x+2)(x^2+x+1) =l ...

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Derivative from First Principle

Evaluate: li...

Question

Evaluate:
$lim x \to 1 (\frac{1}{x^{2} + x - 2} - \frac{x}{x^{3} - 1})$

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Evaluate the following one sided limits:

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

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i .

lim x \to 1 [\frac{x^{2} + 1}{x + 100}]

i i .

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

i i i .

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

i v .

lim x \to 2 [\frac{x^{3} - 2 x^{2}}{x^{2} - 5 x + 6}]

v .

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

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