Download App

Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits4 Marks
Question
Evaluate the following limit: If $\lim\limits_{\text{x}\rightarrow0}{\text{ kx cosec x}}=\lim\limits_{\text{x}\rightarrow0}\text{ x cosec kx,}{}$ find k.
✓

Answer

$\lim\limits_{\text{x}\rightarrow0}{\text{ kx cosec x}}=\lim\limits_{\text{x}\rightarrow0}\text{ x cosec kx,}{}$ $\lim\limits_{\text{x}\rightarrow0}\text{ kx}\frac{1}{\sin\text{x}}=\lim\limits_{\text{x}\rightarrow0}\text{x}\frac{1}{\sin\text{kx}}$ $\text{k}\lim\limits_{\text{x}\rightarrow0}\Big(\frac{\text{x}}{\sin\text{x}}\Big)=\frac{1}{\text{k}}\lim\limits_{\text{x}\rightarrow0}\Big(\frac{\text{kx}}{\sin\text{kx}}\Big)$ $\text{k}=\frac{1}{\text{k}}$ $\text{k}^2=1$ $\text{k}=\pm1$

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 4 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

If $\text{z}_1=2-\text{i}, \ \text{z}_2=-2+\text{i},$ Find $\text{Re}\Big(\frac{\text{z}_1\text{z}_2}{\text{z}_1}\Big)$
→
Find the number of ways of selection 9 balls from 6 red balls, 5 white balls and 5 balls if each selection consists of 3 balls of each colour.
→
The equation of the base of an equilateral triangle is x + y = 2 and its vertex is (2, -1). Find the length and equations of its sides.
→
For any two sets A and B, prove that: A' - B' = B - A.
→
Find the equation of the circle which circumscribes the triangle formed by the lines $x + y = 2, 3x - 4y = 6$ and $x - y = 0$.
→
Find the equations of the straight lines each of which passes through the point (3, 2) and cuts off intercepts a and b respectively on X and Y-axes such that a - b = 2.
→
If P(2n − 1, n) : P(2n + 1, n − 1) = 22 : 7 find n.
→
Find the distance of the line 2x + y = 3 from the point (-1, -3) in the direction of the line whose slope is 1.
→
Of the members of three athletic teams in a certain school, 21 are in the basketball team, 26 in hockey team and 29 in the football team. 14 play hockey and basketball, 15 play hockey and football, 12 play football and 8 play all the three game. How many member are there in all?
→
If $2\tan\frac{\alpha}{2}=\tan\frac{\beta}{2},$ prove that $\cos\alpha=\frac{3+5\cos\beta}{5+3\cos\beta}$
→