Consider the function F(x)=∣x∣.
a. (i) State the definitions of continuity and differentiability of a real‐valued function at a point.
b. (ii) Verify whether F(x) is continuous at x=0.
c. (iii) Determine whether F(x) is differentiable at x=0. Give full justification based on the behaviour of the relevant limits.
d. (iv) Interpret geometrically your conclusion in part (iii) with reference to the graph of y=∣x∣. What does this tell you about the tangent at the origin?