If \( f(\theta)=\lim _{n \rightarrow \infty} \sum_{r=0}^{n \theta} \frac{2 r}{n \sqrt{(3 \theta ...
If \( f(\theta)=\lim _{n \rightarrow \infty} \sum_{r=0}^{n \theta} \frac{2 r}{n \sqrt{(3 \theta n-2 r)(n \theta+2 r)}} \) then :
(a) \( f(1)=\frac{\pi}{6} \)
(b) \( f(\theta)=\frac{\theta}{2} \int_{0}^{\theta} \frac{d x}{\sqrt{\theta^{2}-\left(x-\frac{\theta}{2}\right)^{2}}} \)
(c) \( f(\theta) \) is a constant function
(d) \( y=f(\theta) \) is invertible
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
| 2022-10-28 | The number of solution of equation \( \sin ^{-1} x+n \sin ^{-1}(1-x) \) \( =\frac{m \pi}{2} \), ... |
| 2022-10-28 | The polysaccharides made up of glucose monomers are
(a) sucrose, lactose, maltose
(b) chitin, gl... |
| 2022-10-28 | \( \tan ^{-1}\left[\frac{\cos x}{1+\sin x}\right] \) is equal to
(1) \( \frac{\pi}{4}-\frac{x}{2... |
| 2022-10-28 | Which of the following statements about amino acids is incorrect?
(a) Essential amino acids are ... |
| 2022-10-28 | Refer to the given figure and select the correct option regarding it.
(a) C could be Pleurobrach... |
| 2022-10-28 | Net gain of ATP molecules during aerobic respiration of one molecule of glucose is -
(a) 36
(b) ... |
| 2022-10-28 | If \( f(x)=x^{11}+x^{9}-x^{7}+x^{3}+1 \) and \( f\left(\sin ^{-1}(\sin 8)\right)=\alpha \), wher... |
| 2022-10-28 | Find the number of solutins of the equations
\[
(\sin x-1)^{3}+(\cos x-1)^{3}+(\sin x)^{3}=(2 \s... |
| 2022-10-28 | If \( \sin ^{-1}:[-1,1] \rightarrow\left[\frac{\pi}{2}, \frac{3 \pi}{2}\right] \) and \( \cos ^{... |
| 2022-10-28 | The solution of the inequality \( \log _{1 / 2} \sin ^{-1} x\log _{1 / 2} \cos ^{-1} x \) is
(1)... |
| 2022-10-28 | If \( f(\theta)=\lim _{n \rightarrow \infty} \sum_{r=0}^{n \theta} \frac{2 r}{n \sqrt{(3 \theta ... |
| 2022-10-28 | The value of the expression \( \sin ^{-1}\left(\sin \frac{22 \pi}{7}\right) \) \( \cos ^{-1}\lef... |
| 2022-10-28 | The value of \( \sin ^{-1}(\sin 12)+\cos ^{-1}(\cos 12) \) is equal to
(1) zero
(2) \( 24-2 \pi ... |
| 2022-10-28 | The value of \( \sin ^{-1}\left(\cos \left(\cos ^{-1}(\cos x)+\sin ^{-1}(\sin x)\right)\right) \... |
| 2022-10-28 | Paragraph for Question
Let \( A B C \) be a triangle inscribed in a circle and let \( l_{a}=\fra... |
| 2022-10-28 | If \( \left|\cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)\right|\frac{\pi}{3} \), then
(1) \( x... |
| 2022-10-28 | The number of solutions of the system of equations :
\[
\begin{aligned}
2 \sin ^{2} x+\sin ^{2} ... |
| 2022-10-28 | Let \( I=\int_{0}^{\pi} x^{6}(\pi-x)^{8} d x \), then \( \frac{\pi^{15}}{\left({ }^{15} C_{9}\ri... |
| 2022-10-28 | Consider all functions \( f:\{1,2,3,4\} \rightarrow\{1,2,3,4\} \) which are one-one, onto and sa... |
| 2022-10-28 | In \( \triangle A B C \), if \( \angle C=90^{\circ} \), then \( \frac{a+c}{b}+\frac{b+c}{a} \) i... |
| 2022-10-28 | In a \( \triangle A B C \), if \( a^{2} \sin B=b^{2}+c^{2} \), then:
(a) \( \angle A \) is obtus... |
0