If alpha is the interior angle of a regular o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The interior angle of a regular octagon is given by $\alpha = \frac{(8-2) 	imes 180^{\circ}}{8} = 135^{\circ} = \frac{3\pi}{4}$.We need to evalua

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(D) The interior angle of a regular octagon is given by $\alpha = \frac{(8-2) 	imes 180^{\circ}}{8} = 135^{\circ} = \frac{3\pi}{4}$.We need to evaluate $\lim_{	heta 	o (\frac{3\pi}{4})^+} \frac{	an 	heta - 1}{[\sin 	heta + \cos 	heta]}$.As $	heta 	o (\frac{3\pi}{4})^+$,$	heta$ is slightly greater than $\frac{3\pi}{4}$.In this interval,$\sin 	heta + \cos 	heta = \sqrt{2} \sin(	heta + \frac{\pi}{4})$.As $	heta 	o (\frac{3\pi}{4})^+$,$	heta + \frac{\pi}{4} 	o \pi^+$,so $\sin(	heta + \frac{\pi}{4})$ is a small negative value.Thus,$\sin 	heta + \cos 	heta$ is a small negative value,specifically in the range $(-1, 0)$.Therefore,$[\sin 	heta + \cos 	heta] = -1$.The limit becomes $\lim_{	heta 	o (\frac{3\pi}{4})^+} \frac{	an 	heta - 1}{-1} = -(	an(\frac{3\pi}{4}) - 1) = -(-1 - 1) = -(-2) = 2$.

If $\alpha$ is the interior angle of a regular octagon,then $\lim_{\theta \to \alpha^+} \frac{\tan \theta - 1}{[\sin \theta + \cos \theta]}$ is equal to (Note: $[k]$ denotes the greatest integer less than or equal to $k$).

Similar Questions

$\lim _{x}$ ${\rightarrow \infty} \frac{(2 x+1)^{50}+(2 x+2)^{50}+(2 x+3)^{50}+\cdots \cdots+(2 x+100)^{50}}{(2 x)^{50}+(10)^{50}} = \dots$

$\lim _{x \rightarrow \infty}\left(\frac{x+5}{x+2}\right)^{x+3}$ equals

If $f(x) = \begin{cases} \frac{\sin(1+[x])}{[x]}, & \text{for } [x] \neq 0 \\ 0, & \text{for } [x] = 0 \end{cases}$ where $[x]$ denotes the greatest integer function,then $\lim_{x \rightarrow 0^{-}} f(x)$ is equal to

The value of $\mathop {\lim }\limits_{x \to 0} \left( \frac{e^x - 1}{x} \right)$ is

$\mathop {\lim }\limits_{n \to \infty } {\left( {\frac{{{n^2} - n + 1}}{{{n^2} - n - 1}}} \right)^{n(n - 1)}} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module