Using the fact that \( x^{1 / x} \) in decreasing in \( (e, \infty) \) which of the numerical in...
Using the fact that \( x^{1 / x} \) in decreasing in \( (e, \infty) \) which of the numerical inequalities can be concluded -
(a) \( e^{\pi}\pi^{e} \)
(b) \( \sqrt[5]{5}\sqrt[6]{6} \)
(c) \( \left(\sin 3^{\circ}\right)^{\sin 5^{\circ}}\left(\sin 5^{\circ}\right)^{\sin 3^{\circ}} \)
(d) \( \left(\tan 75^{\circ}\right)^{\tan 80^{\circ}}\left(\tan 80^{\circ}\right)^{\tan 75^{\circ}} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
| 2023-06-08 | If \( f \phi, \psi \) are continuous in \( [a, b] \) and derivable in \( ] a, b[ \) then show th... |
| 2023-06-08 | Themass of a cell culture at time \( t \) is given by, \( M(t)=\frac{3}{1+4 e^{-1}} \)
(a) Find ... |
| 2023-06-08 | Show that equation \( e^{x}+x^{5}+5 x+7=0 \) has only one real root. |
| 2023-06-08 | Discuss the monotonicity of
\[
y=\int_{\frac{5 \pi}{3}}^{x}(6 \cos u-2 \sin u) d u \text { in }\... |
| 2023-06-08 | If \( \forall h \in R-\{0\} \), two distinct tangents can be drawn from the points \( (2+h, 3 h-... |
| 2023-06-08 | A particle moves in a straight line with position relative to some origin \( \mathrm{O} \) given... |
| 2023-06-08 | Alongside is a land and sea profile where the \( \mathrm{x} \)-axis is sea level. The function \... |
| 2023-06-08 | Find the equation of tangent and normal to the curve \( f(x)=\left[\begin{array}{clc}x-2 & \text... |
| 2023-06-08 | If the distance of the point on \( y=x^{4}+3 x^{2}+2 x \) which is nearest to the line \( y=2 x-... |
| 2023-06-08 | \( \begin{array}{ll}\text { Comprehension } & : \text { Read the following write up }\end{array}... |
| 2023-06-08 | Using the fact that \( x^{1 / x} \) in decreasing in \( (e, \infty) \) which of the numerical in... |
| 2023-06-08 | Let \( f(x)=\frac{(x-1)^{2} \cdot e^{x}}{\left(1+x^{2}\right)^{2}} \), then which of the followi... |
| 2023-06-08 | \( h(x)=3 f\left(\frac{x^{2}}{3}\right)+f\left(3-x^{2}\right) \forall x \in(-3,4) \), where \( f... |
| 2023-06-08 | If \( f(x) \) is twice differentiable polynomial function such that \( f(1)=1, f(2)=4, f(3)=9 \)... |
| 2023-06-08 | \[
f: \mathbb{R} \rightarrow \mathbb{R} ; f\left(x^{2}+x+3\right)+2 f\left(x^{2}+2 x+5\right)=8 ... |
| 2023-06-08 | Let \( f(x)=\left\{\begin{array}{cc}x^{3}+x^{2}-10 x & -1 \leq x0 \\ \sin x & 0 \leq x\frac{\pi}... |
| 2023-06-08 | The normal to the curve \( x=a(\cos \theta+\theta \sin \theta), y= \) \( a(\sin \theta-\theta \c... |
| 2023-06-08 | The angle at which the curve \( y=k e^{k x} \) intersects the \( y \)-axis is-
(a) \( \tan ^{-1}... |
| 2023-06-08 | The composite function of \( f_{1}\left(f_{2}\left(f_{3}\left(\ldots \ldots\left(f_{\mathrm{n}}(... |
| 2023-06-08 | Suppose \( \alpha, \beta \) and \( \theta \) are angles satisfying \( 0\alpha\theta\beta\pi / 2 ... |
| 2023-06-08 | If \( f^{\prime}\left(x^{2}-4 x+3\right)0, \forall x \in(2,3) \); then \( f(\sin x) \) is increa... |
0