\[\lim_\theta \to 0 \frac{\sin 3\theta}{\tan 2\theta}\]

\[\lim_\theta \to 0 \frac{\sin 3\theta}{\tan 2\theta}\] \[= \lim_\theta \to 0 \left[ \frac{\sin 3\theta}{3\theta} \times \frac{3\theta}{\frac{\tan 2\theta}{2\theta} \times 2\theta} \right]\]\[ = \frac{3}{2}\]

Lim θ → 0 Sin 3 θ Tan 2 θ - Mathematics

Question

$lim_{θ} \to 0 \frac{\sin 3 θ}{\tan 2 θ}$

Solution

$lim_{θ} \to 0 \frac{\sin 3 θ}{\tan 2 θ}$

$= lim_{θ} \to 0 [\frac{\sin 3 θ}{3 θ} \times \frac{3 θ}{\frac{\tan 2 θ}{2 θ} \times 2 θ}]$
$= \frac{3}{2}$

shaalaa.com

Concept of Limits - Algebra of Limits

Is there an error in this question or solution?

Q 16 Q 15 Q 17

Chapter 29: Limits - Exercise 29.7 [Page 50]

APPEARS IN

RD Sharma Mathematics [English] Class 11

Chapter 29 Limits
Exercise 29.7 | Q 16 | Page 50

Video TutorialsVIEW ALL [1]

view
Video Tutorials For All Subjects
Concept of Limits - Algebra of Limits

video tutorial00:08:11

RELATED QUESTIONS

Suppose f(x) = ${\begin{cases} a + b x & x < 1 \\ 4 & x = 1 \\ b - a x & x > 1 \end{cases}$ and if $lim_{x \to 1} f (x) = f (1)$ what are possible values of a and b?

$lim_{x \to 3} \frac{\sqrt{2 x + 3}}{x + 3}$

$lim_{x \to 1} \frac{1 + {(x - 1)}^{2}}{1 + x^{2}}$

$lim_{x \to - 1} (4 x^{2} + 2)$

$lim_{x \to 3} \frac{x^{4} - 81}{x^{2} - 9}$

$lim_{x \to 5} \frac{x^{2} - 9 x + 20}{x^{2} - 6 x + 5}$

$lim_{x \to 0} \frac{{(a + x)}^{2} - a^{2}}{x}$

$lim_{x \to 2} [\frac{1}{x - 2} - \frac{2 (2 x - 3)}{x^{3} - 3 x^{2} + 2 x}]$

$lim_{n \to \infty} \frac{n^{2}}{1 + 2 + 3 + . . . + n}$

$lim_{x \to \infty} \frac{\sqrt{x^{2} + a^{2}} - \sqrt{x^{2} + b^{2}}}{\sqrt{x^{2} + c^{2}} - \sqrt{x^{2} + d^{2}}}$

$lim_{n \to \infty} [\frac{1 + 2 + 3 . . . . . . n - 1}{n^{2}}]$

$lim_{n \to \infty} [\frac{1^{3} + 2^{3} + . . . . n^{3}}{n^{4}}]$

$lim_{x \to 0} \frac{\tan^{2} 3 x}{x^{2}}$

$lim_{x \to 0} \frac{\sin^{2} 4 x^{2}}{x^{4}}$

$lim_{x \to 0} \frac{x \cos x + 2 \sin x}{x^{2} + \tan x}$

$lim_{x \to 0} \frac{\sec 5 x - \sec 3 x}{\sec 3 x - \sec x}$

$lim_{x \to 0} \frac{1 - \cos 2 x + \tan^{2} x}{x \sin x}$

$lim_{x \to 0} \frac{\sqrt{2} - \sqrt{1 + \cos x}}{x^{2}}$

$lim_{x \to 0} \frac{\cos 2 x - 1}{\cos x - 1}$

$lim_{x \to 0} \frac{1 - \cos 2 x}{3 \tan^{2} x}$

$lim_{x \to 0} \frac{5 x + 4 \sin 3 x}{4 \sin 2 x + 7 x}$

$lim_{x \to 0} \frac{\tan 2 x - \sin 2 x}{x^{3}}$

Evaluate the following limit:

$lim_{h \to 0} \frac{{(a + h)}^{2} \sin (a + h) - a^{2} \sin a}{h}$

If $lim_{x \to 0} k x c o s e c x = lim_{x \to 0} x c o s e c k x,$

$lim_{x \to \frac{π}{4}} \frac{1 - \tan x}{x - \frac{π}{4}}$

$lim_{x \to \frac{π}{2}} (\frac{π}{2} - x) \tan x$

$lim_{x \to \frac{π}{4}} \frac{\sqrt{2} - \cos x - \sin x}{{(4 x - π)}^{2}}$

$lim_{x \to \frac{π}{4}} \frac{\cos x - \sin x}{(\frac{π}{4} - x) (\cos x + \sin x)}$

$lim_{x \to \frac{3 π}{2}} \frac{1 + {c o s e c}^{3} x}{\cot^{2} x}$

$lim_{x \to 0^{-}} \frac{\sin x}{\sqrt{x}} .$

$lim_{x \to 0} \frac{(1 - \cos 2 x) \sin 5 x}{x^{2} \sin 3 x} =$

$lim_{x \to \infty} \frac{\sin x}{x}$ equals

$lim_{x \to π / 4} \frac{\sqrt{2} \cos x - 1}{\cot x - 1}$ is equal to

Evaluate the following limit:

$lim_{x \to 7} [\frac{(\sqrt[3]{x} - \sqrt[3]{7}) (\sqrt[3]{x} + \sqrt[3]{7})}{x - 7}]$

Evaluate the following limits: $lim_{x \to 0} [\frac{\sqrt[3]{1 + x} - \sqrt{1 + x}}{x}]$

Evaluate the Following limit:

$lim_{x \to 3} [\frac{\sqrt{x + 6}}{x}]$

Evaluate the following limits: $lim_{x \to 3} [\frac{\sqrt{x + 6}}{x}]$

Evaluate the Following limit:

$lim_{x \to 7} [\frac{(\sqrt[3]{x} - \sqrt[3]{7}) (\sqrt[3]{x} + \sqrt[3]{7})}{x - 7}]$

Lim θ → 0 Sin 3 θ Tan 2 θ - Mathematics

Advertisements

Advertisements

Question

Solution

APPEARS IN

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Select a course

Lim θ → 0 Sin 3 θ Tan 2 θ - Mathematics

Advertisements

Advertisements

Question

SolutionShow Solution

APPEARS IN

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Select a course

Solution