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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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Factorization Method Form to Remove Indeterminate Form

Standard XII Mathematics

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