Evaluate the following limits: `lim_(x -> oo) 3/(x - 2) - (2x + 11)/(x^2 + x - 6)`

`lim_(x -> oo) 3/(x - 2) - (2x + 11)/(x^2 + x - 6) = lim_(x -> oo) (3/(x - 2) - (2x + 11)/((x + 3)(x - 2)))` = `lim_(x -> oo) (3(x + 3) - (2x + 11))/((x + 3)(x - 2))` = `lim_(x -> oo) (3x + 9 - 2x - 11)/((x + 3)(x - 2))` = `lim_(x -> oo) (x - 2)/((x + 3)(x - 2))` = `lim_(x -> oo) 1/(x + 3)` = `1/oo` `lim_(x -> oo) 3/(x - 2) - (2x + 11)/(x^2 + x - 6)` = 0

Evaluate the following limits: limx →∞3x-2-2x+11x2+x-6 - Mathematics

प्रश्न

Evaluate the following limits:

$lim_{x \to \infty} \frac{3}{x - 2} - \frac{2 x + 11}{x^{2} + x - 6}$

बेरीज

उत्तर

$lim_{x \to \infty} \frac{3}{x - 2} - \frac{2 x + 11}{x^{2} + x - 6} = lim_{x \to \infty} (\frac{3}{x - 2} - \frac{2 x + 11}{(x + 3) (x - 2)})$

= $lim_{x \to \infty} \frac{3 (x + 3) - (2 x + 11)}{(x + 3) (x - 2)}$

= $lim_{x \to \infty} \frac{3 x + 9 - 2 x - 11}{(x + 3) (x - 2)}$

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

= $lim_{x \to \infty} \frac{1}{x + 3}$

= $\frac{1}{\infty}$

$lim_{x \to \infty} \frac{3}{x - 2} - \frac{2 x + 11}{x^{2} + x - 6}$ = 0

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Q 3 Q 2 Q 4

पाठ 9: Differential Calculus - Limits and Continuity - Exercise 9.3 [पृष्ठ १११]

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पाठ 9 Differential Calculus - Limits and Continuity
Exercise 9.3 | Q 3 | पृष्ठ १११

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Evaluate the following limits: limx →∞3x-2-2x+11x2+x-6 - Mathematics

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Evaluate the following limits: limx →∞3x-2-2x+11x2+x-6 - Mathematics

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