Find the equation of the plane passing through the point $$(2,1,3)$$ and perpendicular to the planes $$x-2 y+2 z+3=0$$ and $$3 x-2 y+4 z-4=0$$.

If $$f(x)=\left\{\begin{array}{cc}\frac{e^{\alpha x}-e^x-x}{x^2}, & x \neq 0 \\ \frac{3}{2}, & x=0\end{array}\right.$$

Find the value of $$\alpha$$ for which the function $$f$$ is continuous

The value of $$k(k > 0)$$, for which the function $$f(x)=\frac{\left(e^x-1\right)^4}{\sin \left(\frac{x^2}{k^2}\right) \log \left(1+\frac{x^2}{2}\right)}$$, where $$x \neq 0$$ and $$f(0)=8$$

If $$\log \left(\sqrt{1+x^2}-x\right)=y\left(\sqrt{1+x^2}\right)$$, then $$\left(1+x^2\right) \frac{d y}{d x}+x y$$ is equal to