Download App

Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits3 Marks
Question
Evaluate the following limit: $\lim\limits_{\theta\rightarrow0}\frac{\sin3\theta}{\tan2\theta}$
✓

Answer

$\lim\limits_{\theta\rightarrow0}\frac{\sin3\theta}{\tan2\theta}$ $=\frac{\lim\limits_{\theta\rightarrow0}\sin3\theta}{\lim\limits_{\theta\rightarrow0}\tan2\theta}$ $=\frac{\lim\limits_{3\theta\rightarrow0}\frac{\sin3\theta}{3\theta}\times3\theta}{\lim\limits_{2\theta\rightarrow0}\frac{\tan2\theta}{2\theta}\times2\theta}$ $=\frac{\Big(\lim\limits_{3\theta\rightarrow0}\frac{\sin3\theta}{3\theta}\Big)}{\Big(\lim\limits_{2\theta\rightarrow0}\frac{\tan2\theta}{2\theta}\Big)}\times\frac{3\theta}{2\theta}$$=\frac11\times\frac32$ $\Big[\because\lim\limits_{\text{x}\rightarrow0}\frac{\sin\text{x}}{\text{x}}=1\text{ and }\lim\limits_{\text{x}\rightarrow0}\frac{\tan\text{x}}{\text{x}}=1\Big]$
$=\frac32$

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 3 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 A.M. between: 7 and 13
→
Find the coordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse $9x^2 + 4y^2 = 36.$
→
If f is a function satisfying f (x+y) = f (x) f (y) for all x, y $ \in $ N such that f (1) = 3 and $\sum\limits_{x = 1}^n f (x) = 120$ find the value of n.
→
Differentiate the following functions with respect to x:$\frac{\sec\text{x}-1}{\sec\text{x}+1}$
→
How many terms of the A.P., $- 6 , \frac { - 11 } { 2 } , - 5 , \ldots$are needed to give the sum -25?
→
Find the $4^{th}$ term in the expansion of $(x - 2y)^{12}$.
→
The longest side of a triangle is three times the shortest side and third side is 2 cm shorter than the longest side if the perimeter of the triangles at least 61 cm, find the minimum length of the shortest-side.
→
If a function f : R → R be defined by: $\text{f(x)}=\begin{cases}3\text{x}-2,&\text{ x}<0\\1,&\text{x}=0\\4\text{x}+1,&\text{ x}>0\end{cases}$ Find: f(1), f(-1), f(0) and f(2)
→
If ${^\text{15}}\text{C}_{\text{r}}:{^\text{15}}\text{C}_{\text{r-1}},=11:5,$ Find r.
→
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
→