Download App

Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits3 Marks
Question
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\tan8\text{x}}{\sin2\text{x}}$
✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\tan8\text{x}}{\sin2\text{x}}$ $=\frac{\lim\limits_{\text{x}\rightarrow0}{\tan8\text{x}}{}}{\lim\limits_{\text{x}\rightarrow0}{\sin2\text{x}}}$ $=\frac{\lim\limits_{\text{x}\rightarrow0}\frac{\tan8\text{x}}{8\text{x}}\times8\text{x}}{\lim\limits_{\text{x}\rightarrow0}\frac{\sin2\text{x}}{2\text{x}}\times2\text{x}}$ $\big[\because\sin3\text{x}=3\sin\text{x}-4\sin^3\text{x}\big]$ $=\frac{\lim\limits_{8\text{x}\rightarrow0}\frac{\tan8\text{x}}{8\text{x}}\times\frac{8\text{x}}{2\text{x}}}{\lim\limits_{2\text{x}\rightarrow0}\frac{\sin2\text{x}}{2\text{x}}}$ $\begin{bmatrix}\because\text{x}\rightarrow 0 \\8\text{x}\rightarrow0 \\2\text{x}\rightarrow0 \end{bmatrix}$ $=\frac{1\times\frac82}{1}$ $\Big[\because\ \lim\limits_{\text{x}\rightarrow0}\frac{\sin\text{x}}{\text{x}}=1\text{ and }\lim\limits_{\text{x}\rightarrow0}\frac{\tan\text{x}}{\text{x}}=1\Big]$ $=\frac82$ $=4$

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

Differentiate the following function with respect to $(\text{x})$:$\frac{\cos(\text{x}-2)}{\sin\text{x}}$
→
Find the sum to n terms of the series $1 \times 2+2 \times 3+3 \times 4+4 \times 5+. .$
→
A beam is supported at its ends by supports which are $12$ metres apart. Since the load is concentrated at its centre, there is a deflection of $3$ cm at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection $1$ cm?
→
Find the number of ways in which one can post 5 letters in 7 letter boxes.
→
Find the distance between $P(x_1, y_1)$ and $Q(x_2, y_2)$ when PQ is parallel to the y-axis
→
Find the distance of the point (1, 2) from the straight line with slope 5 and passing through the point of intersection of x + 2y = 5 and x - 3y = 7.
→
If $\sin\text{A}=\frac{12}{13}$ and $\sin\text{B}=\frac{4}{5}$ Where $\frac{\pi}{2}<\text{A}<\pi$and $0<\text{B}<\frac{\pi}{2},$ find the following:
→
Using section formula, show that the points A(2, -3, 4)b(-1, 2, 1) and $C\left( {0,\frac{1}{3},2} \right)$ are collinear.
→
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
$\frac{{{x^2}}}{{100}} + \frac{{{y^2}}}{{400}} = 1$
→
  1. If $\Big(\frac{\text{a}}{3}+1,\text{b}-\frac{2}{3}\Big)=\Big(\frac{5}{3},\frac{1}{3}\Big),$ find the values of a and b.
  2. f(x + 1, 1) = (3, y - 2), find the values of x and y.
→