If f(x) = sqrt{x^2 + x} + frac{tan^2 alpha}{s | vedclass

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

Question

(A) We are given $f(x) = \sqrt{x^2 + x} + \frac{	an^2 \alpha}{\sqrt{x^2 + x}}$.Since $x > 0$,$\sqrt{x^2 + x} > 0$. Also,$	an^2 \alpha > 0$ for $\alp

Vedclass · Accepted Answer

$2 	an \alpha$

Vedclass · Answer

(A) We are given $f(x) = \sqrt{x^2 + x} + \frac{	an^2 \alpha}{\sqrt{x^2 + x}}$.Since $x > 0$,$\sqrt{x^2 + x} > 0$. Also,$	an^2 \alpha > 0$ for $\alpha \in (0, \pi/2)$.Using the Arithmetic Mean-Geometric Mean $(AM \geq GM)$ inequality for two positive terms $a$ and $b$,we have $\frac{a+b}{2} \geq \sqrt{ab}$,or $a+b \geq 2\sqrt{ab}$.Let $a = \sqrt{x^2 + x}$ and $b = \frac{	an^2 \alpha}{\sqrt{x^2 + x}}$.Then $f(x) = a + b \geq 2\sqrt{a \cdot b}$.$f(x) \geq 2\sqrt{\sqrt{x^2 + x} \cdot \frac{	an^2 \alpha}{\sqrt{x^2 + x}}}$.$f(x) \geq 2\sqrt{	an^2 \alpha}$.Since $\alpha \in (0, \pi/2)$,$	an \alpha > 0$,so $\sqrt{	an^2 \alpha} = 	an \alpha$.Therefore,$f(x) \geq 2 	an \alpha$.

List-$I$	List-$II$
$A$. The number of non-bijective functions from $G \times G$ to $G$	$I$. $24$
$B$. The number of bijective functions from $A$ to $A$	$II$. $0$
$C$. The number of functions from $G$ to $G \times A$	$III$. $1728$
$D$. The number of surjective functions from $A$ to $A \times A$	$IV$. $12$
	$V$. $19683$

If $f(x) = \sqrt{x^2 + x} + \frac{\tan^2 \alpha}{\sqrt{x^2 + x}}$,where $\alpha \in (0, \pi/2)$ and $x > 0$,then the value of $f(x)$ is greater than or equal to:

Similar Questions

The probability that a relation $R$ from $\{x, y\}$ to $\{x, y\}$ is both symmetric and transitive is equal to:

The number of solutions of the equation $2{e^{\left| x \right|}}{\tan ^{ - 1}}\left| x \right| = 1$ is

Let $f : \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \rightarrow \mathbb{R}$ be defined by $f(x) = (\log(\sec x + \tan x))^3$. Then:

Let $A = \{2, 3, 4, 5, 6\}$. Let $R$ be a relation on the set $A \times A$ defined by $(x, y) R (z, w)$ if and only if $x$ divides $z$ and $y \le w$. Then the number of elements in $R$ is . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module