Question

(iv) Prove that the modulus function is continuous at x=0​

Answer 1

Answer:

To show that f(x)=|x| is continuous at 0 , show that limx→0|x|=|0|=0 . Use ε−δ if required, or use the piecewise definition of absolute value. and limx→0−|x|=limx→0−(−x)=0 . ... That is, the derivative does not exist at x=0 .