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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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Factorization Method Form to Remove Indeterminate Form

Standard XII Mathematics

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