Lim x- 9 2x-7- x -3 - 3x-11- x -6

The correct option is B 5 / 7 lim _ x→ 9 2x 7√( x ) +3 3x 11√( x ) +6 #160; let √( x ) =t,when x→ 9,t→ 3 lim _ t→ 3 = 2 t ^ 2 7t ...

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Byju's Answer

Standard XII

Mathematics

Existence of Limit

lim x→ 9 2x-7...

Question

${lim}_{x \to 9} \frac{2 x - 7 \sqrt{x} + 3}{3 x - 11 \sqrt{x} + 6}$

\frac{3}{4}

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\frac{5}{3}

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\frac{5}{7}

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\frac{3}{7}

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Solution

The correct option is B $\frac{5}{7}$
${lim}_{x \to 9} \frac{2 x - 7 \sqrt{x} + 3}{3 x - 11 \sqrt{x} + 6} l e t \sqrt{x} = t, w h e n x \to 9, t \to 3 {lim}_{t \to 3} = \frac{2 t^{2} - 7 t + 3}{3 t^{2} - 11 t + 6}$
Using LHR.
$\Rightarrow \frac{4 t - 7}{6 t - 11} \Rightarrow \frac{12 - 7}{18 - 11} = \frac{5}{7}$

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Similar questions

Q. Evaluate:

lim x \to 2 \frac{\sqrt{x + 7} - 3 \sqrt{2 x - 3}}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3 x - 5}}

Solve :

$(i) \frac{1}{3} x - 6 = \frac{5}{2} (i i) \frac{2 x}{3} - \frac{3 x}{8} = \frac{7}{12} (i i i) (x + 2) (x + 3) + (x - 3) (x - 2) - 2 x (x + 1) = 0 (i v) \frac{1}{10} - \frac{7}{x} = 35 (v) 13 (x - 4) - 3 (x - 9) - 4 (x + 4) = 0 (v i) x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8} (v i i) \frac{3 x - 2}{4} - \frac{2 x + 3}{3} = \frac{2}{3} - x (v i i i) \frac{x + 2}{6} - (\frac{11 - x}{3} - \frac{1}{4}) = \frac{3 x - 4}{12} (i x) \frac{2}{5 x} - \frac{5}{3 x} = \frac{1}{15} (x) \frac{x + 2}{3} - \frac{x + 1}{5} = \frac{x - 3}{4} - 1 (x i) \frac{3 x - 2}{3} + \frac{2 x + 3}{2} = x + \frac{7}{6} (x i i) x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3} (x i i i) \frac{9 x + 7}{2} - (x - \frac{x - 2}{7}) = 36 (x i v) \frac{6 x + 1}{2} + 1 = \frac{7 x - 3}{3}$