Evaluate the following limit: _ x 3 (1 x-3 -3 x^2-3x ) - Vidyadip

Question

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow3}\Big(\frac{1}{\text{x}-3}-\frac{3}{\text{x}^2-3\text{x}}\Big)$

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Answer

$\lim\limits_{\text{x}\rightarrow3}\Big(\frac{1}{\text{x}-3}-\frac{3}{\text{x}^2-3\text{x}}\Big)$$=\lim\limits_{\text{x}\rightarrow3}\Big(\frac{1}{\text{x}-3}-\frac{3}{\text{x}(\text{x}-3)}\Big)$
$=\lim\limits_{\text{x}\rightarrow3}\Big(\frac{\text{x}-3}{\text{x}(\text{x}-3)}\Big)$
$=\lim\limits_{\text{x}\rightarrow3}\Big(\frac{1}{\text{x}}\Big)$
$=\frac{1}{3}$

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