Evaluate the limit-limx-3 1x-3-3x2-3x

Given: nbsp;lim_x→3( 1x 3 3x^2 3x) becomes nbsp;(∞ ∞ ) nbsp;form Using Factorization method lim_x→3( 1x 3 3x^2 3x) ⇒lim_x→3( 1x 3 3x^2 3x) ⇒lim_x→3( ...

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Standard XIII

Mathematics

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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Evaluate the limit: limx→3(1x−3−3x2−3x)

Given: limx→3(1x−3−3x2−3x) becomes (∞−∞) form Using Factorization method limx→3(1x−3−3x2−3x) ⇒limx→3(1x−3−3x2−3x) ⇒limx→3(x−3x2−3x) ⇒limx→3(x−3x(x−3)) ⇒limx→3(1x)=13 Therefore, ⇒limx→3(1x−3−3x2−3x)=13

Evaluate the limit:

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