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Indeterminate Forms

Evaluate the ...

Question

Evaluate the limit:

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

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Solution

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

becomes $(\infty - \infty)$ form

Using Factorization method
$lim x \to 3 (\frac{1}{x - 3} - \frac{3}{x^{2} - 3 x})$

$\Rightarrow lim x \to 3 (\frac{1}{x - 3} - \frac{3}{x^{2} - 3 x})$

$\Rightarrow lim x \to 3 (\frac{x - 3}{x^{2} - 3 x})$

$\Rightarrow lim x \to 3 (\frac{x - 3}{x (x - 3)})$

$\Rightarrow lim x \to 3 (\frac{1}{x}) = \frac{1}{3}$

$T h e r e f o r e,$

$\Rightarrow lim x \to 3 (\frac{1}{x - 3} - \frac{3}{x^{2} - 3 x}) = \frac{1}{3}$

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Indeterminate Forms

Standard XIII Mathematics

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