Evaluate the limit - limx- 2 xx-2 -4x2-2x

We have, lim_x→ 2 ( xx 2 4x^2 2x )=lim_x→ 2 ( x^2 4x^2 2x ) lim_x→ 2 ( x^2 4x^2 2x ) becomes 00 form Using Factorization method =lim_x→ 2 ( x^2 4x^2 2x ) ...

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Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

Evaluate the ...

Question

Evaluate the limit : $lim x \to 2 (\frac{x}{x - 2} - \frac{4}{x^{2} - 2 x})$

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Solution

We have,

$lim x \to 2 (\frac{x}{x - 2} - \frac{4}{x^{2} - 2 x}) = lim x \to 2 (\frac{x^{2} - 4}{x^{2} - 2 x})$

$lim x \to 2 (\frac{x^{2} - 4}{x^{2} - 2 x}) b e c o m e s \frac{0}{0} f o r m$

Using Factorization method

$= lim x \to 2 (\frac{x^{2} - 4}{x^{2} - 2 x})$

$= lim x \to 2 (\frac{(x - 2) (x + 2)}{x (x - 2)})$

$[∵ (a^{2} - b^{2}) = (a + b) (a - b)]$

$= lim x \to 2 (\frac{(x + 2)}{x})$

$= \frac{2 + 2}{2} = \frac{4}{2} = 2$

Therefore,

$∴ lim x \to 2 (\frac{x}{x - 2} - \frac{4}{x^{2} - 2 x}) = 2$

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

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Factorization Method Form to Remove Indeterminate Form

Standard XII Mathematics

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Evaluate the limit : limx→2(xx−2−4x2−2x)

We have, limx→2(xx−2−4x2−2x)=limx→2(x2−4x2−2x) limx→2(x2−4x2−2x) becomes 00 form Using Factorization method =limx→2(x2−4x2−2x) =limx→2((x−2)(x+2)x(x−2)) [∵(a2−b2)=(a+b)(a−b)] =limx→2((x+2)x) =2+22=42=2 Therefore, ∴limx→2(xx−2−4x2−2x)=2

Evaluate the limit : $lim x \to 2 (\frac{x}{x - 2} - \frac{4}{x^{2} - 2 x})$