Evaluate the following limit: _ 0 3 2 - Vidyadip

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 "3 Marks Question" from Limits→Limits — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Define the real valued function f : R – {0} $\rightarrow$ R defined by $\begin{equation} f(x)=\frac{1}{x} \end{equation}$, x $\in$R – {0}. Complete the Table given below using this definition. What is the domain and range of this function?

x	–2	–1.5	–1	–0.5	0.25	0.5	1	1.5	2
$\begin{equation} y=\frac{1}{x} \end{equation}$	...	...	...	...	...	...	...	...	...

If the sum of three numbers in A.P., is 24 and their product is 440. Find the numbers.

For any two sets A and B, show that the following statements are equevalent:
$\text{A}-\text{B}=\phi.$

Find the mean and variance of the following data.

x_i	92	93	97	98	102	104	109
f_i	3	2	3	2	6	3	3

Solve the system of inequalities:

3x – 7 < 5 + x
11 – 5 x $\le$ 1

and represent the solutions on the number line.

Find the sum of the following series to n terms:
2² + 4² + 6² + 8² + ....

Find the equation of a line drawn perpendicular to the line $\frac{x}{4}+\frac{y}{6}=1$ through the point where it meets the Y-axis.

If the sum of three numbers in A.P. is 24 and their product is 440, find the numbers.

Find the domain of the following real valued functions of real variable:
$\text{f(x)}=\frac{2\text{x}+1}{\text{x}^2-9}$

Two plants A and B of a factory show following results about the number of workers and the wages paid to them:

	Plant A	Plant B
No. of workers	5000	6000
Average monthly wages	₹ 2500	₹ 2500
Variance of distribution of wages	81	100

In which plant A or B is there greater variability in individual wages?