Evaluate the following limit: _ x 0 2x- +x - Vidyadip

Question

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{2\text{x}-\sin\text{x}}{\tan\text{x}+\text{x}}$

✓

Answer

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

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 "Solve the Following Question.(2 Marks)" from Limits→Limits — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Prove that:
$\sin23^\circ+\sin37^\circ=\cos7^\circ$

Prove that:
$\sin\Big(\frac{4\pi}{9}+\text{7}\Big)\cos\Big(\frac{\pi}{9}+\text{7}\Big)-\cos\Big(\frac{4\pi}{9}+\text{7}\Big)\sin\Big(\frac{\pi}{9}+\text{7}\Big)=\frac{\sqrt{3}}{2}$$ $

How many 3-digit numbers are there, with distinct digits, with each digit odd?

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow3}\Big(\frac{1}{\text{x}-3}-\frac{3}{\text{x}^2-3\text{x}}\Big)$

Find what the following equations become when the origin is shifted to the point $(1, 1)$?
$x^2 + y^2 − x + 2y = 0$

$\sum_{r=0}^{\infty}(-8)\left(-\frac{1}{2}\right)^r$

The probability that a student will pass in French is 0.64, will pass in Sociology is 0.45 and will pass in both is 0.40. What is the probability that the student will pass in at least one of the two subjects?

Prove that:
$\frac{\cos(2\pi+\text{x})\text{cosec}(2\pi+\text{x})\tan\Big(\frac{\pi}{2}+\text{x}\Big)}{\sec\Big(\frac{\pi}{2}+\text{x}\Big)\cos\text{x}\cot(\pi+\text{x})}=1$

A fair die is thrown. What are the odds in favour of getting a number which is a perfect square in uppermost face of die?

Find the value of k, if the length of the tangent segment from the point (8, -3) to the circle

$x^2+y^2-2 x+k y-23=0$ is $\sqrt{ } 10$.