Prove that the function `f(x){2+x; if x >= 0 2-x; if x < 0` is not differentiable at `x = 0.`

Prove that the function f(x) = 2x + 3 is continouns at x = 1 .

Prove that the function f(x)={x/(|x|+2x^2),x!=0 and k ,x=0 remains discontinuous at x=0 , regardless the choice of k

Prove that the function f(x) = {:{((sinx)/x , x < 0),(x^2 +1, x ge0):} is continuous.

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

Prove that the function f defined by f(x) = x^3 + x^2 -1 is a continuous function at x= 1.

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

Prove that the function f(x)={x/(|x|+2x^2),\ \ \ x!=0k ,\ \ \ x=0 remains discontinuous at x=0 , regardless the choice of k .

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

Prove that the function f(x)=2x-5 is continuous at x=-2

Prove that the function f(x)= {:{((sinx)/x , xlt 0), (x^(2)+1, x ge 0):} in x belongs to R is continuous