Tag: maths

If $f\left( x \right) =\sqrt { { x }^{ 2 }-2x+1 } $, then

The value of sin $ 2^o $ is approximately

Derivative of $(\sin x)^x + \sin^{-1} \sqrt{x}$ with respect to $x$ is

Let f(x) be a differentiable function satisfying $f(x+y)=f(x)+f(y)\forall x, y \in R$ and $f(0)=1$ then $\displaystyle\lim _{x\rightarrow 0}\dfrac{2^{f(\tan^2x)}-2^{f(\sin^2x)}}{x^3f(\sin x)}$ equals to?

If $t={ \sin {  }  }^{ -1 }{ 2 }^{ s }$ Then $\dfrac { ds }{ dt }$ is equal to

If $u=e^{x}(xcosy-ysiny)$ then $\frac{d^{2}y}{dx^{2}}+\frac{d^{2}u}{dy^{2}}=0$.

If $U=tan^{-1}(\dfrac{x^3+y^3}{x+y})$ , then $x\dfrac{du}{dx}+y\dfrac{du}{dy}=sinu$.

If $y=\sqrt{x}-\dfrac{1}{\sqrt{x}}$, then $2x\dfrac{dy}{dx}+y$=

If $x\sqrt {1+y}+y\sqrt {1+x}=0$ then  $\dfrac {dy}{dx}=\dfrac {1}{(1+x)^{2}}$

Let $f(x)$ be a function continuous on $[1, 2]$ and differentiable on $(1, 2)$ satisfying $f(1)=2, f(2)=3$ and $f'(x)\ge 1\forall x\in (1, 2)$. Define $g(x)=\displaystyle \int _{1}^{x}{f(t)dt}\forall x\in [1, 2]$ then the greatest value of  $g(x)$ on $[1, 2]$ is-