Answer the following questions related to continuity and removable discontinuities.
MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
Answer the following questions related to continuity and removable discontinuities.
(a) Part 1: (i) State the mathematical condition for a real-valued function f to be continuous at x=c.
(b) Part 2: (ii) Explain what is meant by a removable discontinuity in the graph of a function. In your explanation, indicate how such a discontinuity can be eliminated by suitable redefinition of the function at that point.
(c) Part 3: (iii) The function f is defined by f(x)=xsinx,x=0, and is not defined at x=0. Without performing any numerical calculation, explain whether the discontinuity at x=0 is removable. Give a reason based on the concept of limits.