A continuous curve is described verbally as follows
MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability
Problem
A continuous curve is described verbally as follows.
• For x<1 the curve approaches but never meets the point (1,2); as x approaches 1 from the left, the y-values approach 2.
• At x=1 the graph has a solid dot at the point (1,5).
• For x>1 the curve originates at an open circle at (1,5) and, as x approaches 1 from the right, the y-values approach 5.
Answer the following questions about the behavior of the function y=f(x) depicted by this description.
(a) Evaluate x→1−limf(x) and x→1+limf(x). Clearly state each value or indicate if a limit does not exist.
(b) Determine x→1limf(x) and explain your reasoning.
(c) State f(1).
(d) Classify the type of discontinuity that occurs at x=1. Justify your classification in words using the results from parts (a)–(c).