Show that the function `f(x) = 2x - |x|` is continuous at `x = 0`

Prove that the function f(x) =2x-|x| is continuous at x=0.

Show that the function f(x) = |sinx+cosx| is continuous at x = pi .

Show that the function f(x)=2x-|x| is continuous but not differentiable at x=0

Show that the given function f(x) = |2 - 3x + |x|| is continuous for every x in R

Show that the function f(x)={|2x-3|[x]x 0 is continuous but not differentiable at x=1

Show that the function f(x)=|x-2| is continuous but not differentiable at x=2.

Show that the function f(x) =x^2 is continuous and differentiable at x=2.

Show that f(x)=|x| is continuous at x=0

A function f(x) satisfies the following property: f(x.y)=f(x)f(y). Show that the function f(x) is continuous for all values of x if it is continuous at x=1

Show that the function f defined as follows, is continuous at x=2 , but not differentiable: f(x)={3x-2 2x^2 5x 0 2