91Ó°ÊÓ

Prove that the function \(f(x)=5 x-3\) is continuous at \(x=0\), at \(x=-3\) and at \(x=5\).

Verify Rolle's theorem for the function \(f(x)=x^{2}+2 x-8, x \in[-4,2]\).

If \(x\) and \(y\) are connected parametrically by the equations given in Exercises 1 to 10 , without eliminating the parameter, Find \(\frac{d y}{d x}\). $$ x=4 t, y=\frac{4}{t} $$

Prove that the function \(f\) given by $$f(x)=|x-1|, x \in \mathbf{R}$$ is not differentiable at \(x=1\)

Show that the function defined by \(g(x)=x-[x]\) is discontinuous at all integral points. Here \([x]\) denotes the greatest integer less than or equal to \(x\).

Is the function defined by \(f(x)=x^{2}-\sin x+5\) continuous at \(x=\pi\) ?

Show that the function defined by \(f(x)=\cos \left(x^{2}\right)\) is a continuous function.

Find all the points of discontinuity of \(f\) defined by \(f(x)=|x|-|x+1|\).