Download App

Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits3 Marks
Question
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\text{x}\cos\text{x}+2\sin\text{x}}{\text{x}^2+\tan\text{x}}$
✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\text{x}\cos\text{x}+2\sin\text{x}}{\text{x}^2+\tan\text{x}}$ Dividing each term by x $=\lim\limits_{\text{x}\rightarrow0}\frac{\cos\text{x}+\frac{2\sin\text{x}}{\text{x}}}{\text{x}+\frac{\tan\text{x}}{\text{x}}}$ $=\frac{\lim\limits_{\text{x}\rightarrow0}\cos\text{x}+\lim\limits_{\text{x}\rightarrow0}\frac{2\sin\text{x}}{\text{x}}}{\lim\limits_{\text{x}\rightarrow0}\text{x}+\lim\limits_{\text{x}\rightarrow0}\frac{\tan\text{x}}{\text{x}}}$ $=\frac{\cos0+2\lim\limits_{\text{x}\rightarrow0}\frac{\sin\text{x}}{\text{x}}}{0+\lim\limits_{\text{x}\rightarrow0}\frac{\tan\text{x}}{\text{x}}}$ $=\frac{1+2}{0+1}=3$ $\Big[\because\lim\limits_{\text{x}\rightarrow0}\frac{\sin\text{x}}{\text{x}}=1,\lim\limits_{\text{x}\rightarrow0}\frac{\tan\text{x}}{\text{x}}=1\Big]$ $=3$

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 sum to n terms in each of the series in whose $n^{th}$ terms is given by $(2n - 1)^2$
→
Find the slope of the tangent to the curve $\text{f}(\text{x})=\text{2x}^6+\text{x}^4-1$ at$\text{x}=1$
→
If $P(n)$ is the statement "$n^2 + n$ is even", and if $P(r)$ is true, then $P(r + 1)$ is true.
→
Find the sum of the series up to n terms .$6 +. 66 + .666+…$
→
Insert $6$ geometric means between $27$ and $\frac{1}{81}.$
→
In a group of 950 person, 750 can speak Hindi and 460 can speak English. Find: how many can speak both Hindi and English.
→
Solve the inequality graphically in a two-dimensional plane: 3y – 5x < 30
→
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 A = {1, 2} and B = {1, 3}, find A × B and B × A.
→
Prove that : sin 3x + sin 2x - sin x $ = 4\sin \;x\cos \frac{x}{2}\cos \frac{{3x}}{2}$
→