Download App

Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
Question
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\sin\text{x}^\circ}{\text{x}^\circ}$
✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\sin\text{x}^\circ}{\text{x}^\circ}$
$=\lim\limits_{\text{x}\rightarrow0}\frac{{\sin\frac{\text{x}\times\pi}{180}}}{{\text{x}}\times\frac{\pi}{180}}$ $\Big[\because1^\circ=\frac{\pi}{180}\text{ radious}\Big]$
$=\lim\limits_{{\frac{\pi\text{x}}{180}}\rightarrow0}\frac{\sin\frac{\text{x}\times\pi}{180}}{\frac{\pi\text{x}}{180}}$ $\Big[\because\text{if x}\rightarrow0\text{ then }\frac{\pi\text{x}}{180}\rightarrow0\Big]$
$=1$ $\Big[\because\ \lim\limits_{\text{x}\rightarrow0}\frac{\tan\text{x}}{\text{x}}=1\Big]$

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

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{3\sin2\text{x}+2\text{x}}{3\text{x}+2\tan3\text{x}}$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{5^\text{x}+3^\text{x}+2^\text{x}-3}{\text{x}}$
→
Find the number of arranging 11 distinct objects taken 4 at a time so that a specified object (a) always occurs (B)never occurs
→
If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.
→
Verify that $f$ and $g$ are inverse functions of each other, where

$\mathrm{f}(\mathrm{x})=\frac{x-7}{4}, \mathrm{~g}(\mathrm{x})=4 \mathrm{x}+7$

→
Prove that $1+\tan \theta \tan \frac{\theta}{2}=\sec \theta$
→
Find the inverse relation $R ^{-1}$ in the following case:
$R$ is a relation from $\{11,12,13\}$ to $(8,10,12\}$ defined by $y=x-3$.
→
Find the equation of the line whose x-intercept is 3 and which ¡s perpendicular to the line 3x – y + 23 = 0.
→
Find the angle between hour-hand and minute-hand in a clock at : ten past eleven
→
Solve the following system of equations in R.
x - 2 > 0, 3x < 18
→