Download App

Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits2 Marks
Question
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{3\sin2\text{x}+2\text{x}}{3\text{x}+2\tan3\text{x}}$
✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{3\sin2\text{x}+2\text{x}}{3\text{x}+2\tan3\text{x}}$ $=\lim\limits_{\text{x}\rightarrow0}\frac{3\frac{\sin\text{x}}{\text{x}}+2}{3+2\tan\frac{3\text{x}}{\text{x}}}$ $=\frac{\lim\limits_{\text{x}\rightarrow0}\frac{3\sin2\text{x}}{\text{x}}+\lim\limits_{\text{x}\rightarrow0}2}{\lim\limits_{\text{x}\rightarrow0}3+\lim\limits_{\text{x}\rightarrow0}\frac{2\tan3\text{x}}{\text{x}}}$ $=\frac{\Big(3\lim\limits_{2\text{x}\rightarrow0}\frac{\sin2\text{x}}{2\text{x}}\times2\Big)+2}{3+\Big(2\times\lim\limits_{\text{x}\rightarrow0}\frac{\tan3\text{x}}{3\text{x}}\times3\Big)}$ $=\frac{(3\times2)+2}{3+(2\times3)}$ $\Big[\because\ \lim\limits_{\text{x}\rightarrow0}\frac{\sin\text{x}}{\text{x}}=1\text{ also }\lim\limits_{\text{x}\rightarrow0}\frac{\tan\text{x}}{\text{x}}=1\Big]$ $=\frac{8}{9}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 2 marks)" from Limits→Limits — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the equation of two straight lines which are parallel to x + 7y + 2 = 0 and at unit distance from the point (1, -1).
→
In triangle ABC, prove the following: $\frac{\text{a}-\text{b}}{\text{a + b}}=\frac{\tan\big(\frac{\text{A}-\text{B}}{2}\big)}{\tan\big(\frac{\text{A}+\text{B}}{2}\big)}$
→
What is the value of y so that the line through (3, y) and (2, 7) is parallel to the line through (-1, 4) and (0, 6)?
→
Evaluate the following: $\text{i}^{37}+\frac{1}{\text{i}^{67}}$
→
Write the sets $\Big\{\frac{1}{2},\frac{2}{5},\frac{3}{10},\frac{4}{17},\frac{5}{26},\frac{6}{37},\frac{7}{50}\Big\}$ in the set-builder form.
→
Solve: cos x = $\frac{1}{2}$
→
Given statements in (a). Identify the statements given below as contrapositive or converse. If you live in Delhi, then you have winter clothes.
  1. ​If you do not have winter clothes, then you do not live in Delhi.
  2. If you have winter clothes, then you live in Delhi.
→
Find the derivative of function $\frac{{ax + b}}{{p{x^2} + qx + r}}$ (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):.
→
If $\frac{1}{8 !}+\frac{1}{9 !}=\frac{x}{10 !}$, find x.
→
Prove that: $\sin47^\circ+\cos77^\circ=\cos17^\circ$
→