A modulus function is everywhere continuous.

A constant and identity function is everywhere continuous.

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.

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

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

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

Modulus function and properties

Assuming that f is everywhere continuous, (1)/(c )int_(ac)^(bc)f((x)/(c ))dx is equal to

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

Show that the function f defined by f(x)=|1-x+|x|| is everywhere continuous.