If $y^{\frac{1}{m}} + y^{\frac{-1}{m}} = 2x$ , then $(x^2 - 1)y_1^{\ 2} =$

A triangle has two fixed vertices A $(a, 0)$ and B$(0, b)$ . Let its third vertex C is moving along the line $x = y$. If $s$ is the area of triangle ABC, then $\dfrac{ds}{dx} =$

The function $f(x) = \tan^{-1}(\sin x + \cos x)$ is an increasing function in the interval.....

The minimum value of $\dfrac{\log x}{x}$ in the interval $(2, \infty)$ is