VSA

If \(f(x)=a(\tan x-\cot x)\), where \(a>0\), then find whether \(f(x)\) is increasing or decreasing function in its domain.

MCQ_SINGLE

The values of \(\lambda\) so that \(f(x)=\sin x-\cos x-\lambda x+C\) decreases for all real values of x are:

SA

Find the intervals in which the function $f(x)=\frac{log~x}{x}$ is strictly increasing or strictly decreasing.

VSA

Determine the values of x for which $f(x)=\frac{x-3}{x+1}$, $x\ne -1$ is an increasing function.

SA

A spherical balloon loses its volume due to escape of air from it in such a way that decrease of volume at any instant is proportional to its surface area. Show that the radius is decreasing at a constant rate.

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