Evaluate the limit- limx- 2 1x-2-2x2-2x

Given : lim_x→ 2 ( 1x 2 2x^2 2x ) Becomes (∞ ∞) form nbsp; Using Factorization method ⇒ nbsp;lim_x→ 2 ( 1x 2 2x^2 2x ) ⇒ nbsp;lim_x→ 2(x 2)x^2 2x ⇒ ...

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Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

Evaluate the ...

Question

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

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Solution

Given : $lim x \to 2 (\frac{1}{x - 2} - \frac{2}{x^{2} - 2 x})$

Becomes $(\infty - \infty)$ form

Using Factorization method

$\Rightarrow lim x \to 2 (\frac{1}{x - 2} - \frac{2}{x^{2} - 2 x})$

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

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

$\Rightarrow lim x \to 2 \frac{1}{x} = \frac{1}{2}$

Therefore,

$lim x \to 2 (\frac{1}{x - 2} - \frac{2}{x^{2} - 2 x}) = \frac{1}{2}$

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Similar questions

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

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Factorization Method Form to Remove Indeterminate Form

Standard XII Mathematics

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Evaluate the limit: limx→2(1x−2−2x2−2x)

Given : limx→2(1x−2−2x2−2x) Becomes (∞−∞) form Using Factorization method ⇒limx→2(1x−2−2x2−2x) ⇒limx→2(x−2)x2−2x ⇒limx→2(x−2)x(x−2) ⇒limx→21x=12 Therefore, limx→2(1x−2−2x2−2x)=12

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