Kindly consider the following <math><mrow><munder><mrow><mi>l</mi><mi>i</mi><mi>m</mi></mrow><mrow><mi>x</mi><mo>→</mo><mn>0</mn></mrow></munder><mfrac><mrow><mi>s</mi><mi>i</mi><mi>n</mi><mo> </mo><mn>2</mn><mi>x</mi><mo>+</mo><mo> </mo><mn>3</mn><mi>x</mi></mrow><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mi>t</mi><mi>a</mi><mi>n</mi><mn>3</mn><mi>x</mi></mrow></mfrac></mrow></math>

This is a Short Answer Type Questions as classified in NCERT ExemplarSol:Given that limx→0sin 2x+ 3x2x+tan3x =limx→0(sin 2x+ 3x2x×2x)(2x+tan3x3x×3x)=limx→0(sin 2x2x+3x2x)×2x(2x3x+tan3x3x)×3x =(lim2x→0sin 2x2x+32)[23+lim3x→0tan3x3x]×23 [?limx→0sinxx=1] =(1+3223+1)×23 [?limx→0tanxx=1] =5/25/3×23=32×23=1

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Maths Class 11th Limits and Derivatives Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Thirteen

Kindly consider the following
$\underset{x \to 0}{l i m} \frac{s i n 2 x + 3 x}{2 x + t a n 3 x}$

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alok kumar singh | Contributor-Level 10

2 months ago

This is a Short Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t \underset{x \to 0}{l i m} \frac{s i n 2 x + 3 x}{2 x + t a n 3 x} \\ = \underset{x \to 0}{l i m} \frac{(\frac{s i n 2 x + 3 x}{2 x} \times 2 x)}{(\frac{2 x + t a n 3 x}{3 x} \times 3 x)} = \underset{x \to 0}{l i m} \frac{(\frac{s i n 2 x}{2 x} + \frac{3 x}{2 x}) \times 2 x}{(\frac{2 x}{3 x} + \frac{t a n 3 x}{3 x}) \times 3 x} \\ = \frac{(\underset{2 x \to 0}{l i m} \frac{s i n 2 x}{2 x} + \frac{3}{2})}{[\frac{2}{3} + \underset{3 x \to 0}{l i m} \frac{t a n 3 x}{3 x}]} \times \frac{2}{3} [? \underset{x \to 0}{l i m} \frac{s i n x}{x} = 1] \\ = (\frac{1 + \frac{3}{2}}{\frac{2}{3} + 1}) \times \frac{2}{3} [? \underset{x \to 0}{l i m} \frac{t a n x}{x} = 1] \\ = \frac{5 / 2}{5 / 3} \times \frac{2}{3} = \frac{3}{2} \times \frac{2}{3} = 1 \end{array}$

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Kindly consider the following
$\underset{x \to 0}{l i m} \frac{s i n 2 x + 3 x}{2 x + t a n 3 x}$