Continuity and ...

If $$x=a\sec^{2}\theta$$, $$y=a\tan^{3}\theta$$ then $$\dfrac {d^{3}y}{dx^{3}}$$

The value of k which makes $$f(x)=\left\{\begin{matrix} \sin\dfrac{1}{x}, x\neq 0\\ k, x=0\end{matrix}\right.$$ continuous at $$x=0$$ is?

If $$x=\cos ec \theta-\sin \theta,y=\cos ec^{n}\theta-\sin^{n}\theta$$ then $$(x^{2}+4)\left(\dfrac {dy} {dx}\right)^{2}-n^{2}y^{2}=$$ 

Let $$f(x) = \underset{0}{\overset{x}{\int}} |2t - 3| dt$$, then $$f$$ is 

Let $$f(x) = \left\{\begin{matrix}x &x < 1 \\ 2 - x & 1 \leq x \leq 2\\ -2 + 3x - x^{2} & x > 2\end{matrix}\right.$$ then $$f(x)$$ is

Range of function $$f(x)-g(x)$$ in [-$$\pi, \pi$$] is-

Which of the following is NOT CORRECT-

$$\sqrt{1+\left(\dfrac{d^2y}{dx^2}\right)^3}=\left(2+\dfrac{dy}{dx}\right)^{1/3}$$

If $$x$$ $$sin$$ $$y$$$$=3 sin y$$ $$+$$ $$4 cos y$$, then $$\frac { dy }{ dx } =$$

Function $$f(x)-g(x)$$ is-