Evaluate the following limit : limx→3[1x-3-9xx3-27] - Mathematics and Statistics

प्रश्न

Evaluate the following limit :

$lim_{x \to 3} [\frac{1}{x - 3} - \frac{9 x}{x^{3} - 27}]$

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उत्तर

$lim_{x \to 3} [\frac{1}{x - 3} - \frac{9 x}{x^{3} - 27}]$

= $lim_{x \to 3} [\frac{1}{x - 3} - \frac{9 x}{(x - 3) (x^{2} + 3 x + 9)}]$

= $lim_{x \to 3} [\frac{x^{2} + 3 x + 9 - 9 x}{(x - 3) (x^{2} + 3 x + 9)}]$

= $lim_{x \to 3} [\frac{x^{2} - 6 x + 9}{(x - 3) (x^{2} + 3 x + 9)}]$

= $lim_{x \to 3} \frac{(x - 3) (x - 3)}{(x - 3) (x^{2} + 3 x + 9)}$

= $lim_{x \to 3} \frac{x - 3}{x^{2} + 3 x + 9} ... . [\begin{matrix} ∵ x \to 3, x \neq 3 \\ ∴ x - 3 \neq 0 \end{matrix}]$

= $\frac{lim_{x \to 3} (x - 3)}{lim_{x \to 3} (x^{2} + 3 x + 9)}$

= $\frac{3 - 3}{3^{2} + 3 \times 3 + 9}$

= 0

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Q II. (2)Q II. (1)Q II. (3)

पाठ 7: Limits - Exercise 7.2 [पृष्ठ १४१]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board

पाठ 7 Limits
Exercise 7.2 | Q II. (2) | पृष्ठ १४१

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Evaluate the following limit : limx→3[1x-3-9xx3-27] - Mathematics and Statistics

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Evaluate the following limit : limx→3[1x-3-9xx3-27] - Mathematics and Statistics

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