The exponential function `a^x; a>0` is everywhere continuous.

A modulus function is everywhere continuous.

A constant and identity function is everywhere continuous.

If the function and the derivative of the function f(x) is everywhere continuous and is given by f(x)={:{(bx^(2)+ax+4", for " x ge -1),(ax^(2)+b", for " x lt -1):} , then

Write an example of a function which is everywhere continuous but fails to be differentiable exactly at five points.

Write an example of a function which is everywhere continuous but fails to be differentiable exactly at five points.

The function f(x)=|cos sx| is everywhere continuous and differentiable everywhere continuous but not differentiable at (2n+1)(pi)/(2),n in Z .neither continuous not differentiable at (2x+1)(pi)/(2),n in Z

The function f(x)=|cos x| is (a) everywhere continuous and differentiable (b) everywhere continuous but not differentiable at (2n+1)pi/2,n in Z(c) neither continuous nor differentiable at (2n+1)pi/2,n in Z(d) none of these

The function f(x)- Icos xl is (a) everywhere continuous and differentiable b) everywhere continuous but not differentiable at (2n t 1) n/2,ne Z (c) neither continuous nor differentiable at (2n + 1)n/2,ne Z (d) none of these

The function f(x)=x-[x], where | denotes the greatest integer function is (a) continuous everywhere (b) continuous at integer points only ( continuous at non- integer points only (d) differentiable everywhere

Prove that the function f(x)={(sin x)/(x),quad x =0 is everywhere continuous.