Limits, Continuity & Differentiability
General
Grade 12
Question:
<p>limx→c f(x) does not exist when LHL ̸= RHL. Which of the following holds?</p>
f(x) = [x] -[2x -1]; c = 3
f(x) = [x] -x, c = 1
f(x) = {x}2 -{-x}2, c = 0
f(x) = tan(sgn x) sgn x, c = 0
Step-by-Step Solution
Key Concept: General
<p>• (A) For c = 3: RHL = [3+] -[5+] = 3 -5 = -2. LHL = [3-] -[5-] = 2 -4 = -2. Limit</p> exists. • (B) For c = 1: RHL = [1+] -1.1 = -0.1. LHL = [0.9] -0.9 = -0.9. DNE. • (C) For c = 0: RHL = {0.1}2-{0.9}2 = 0.01-0.81 = -0.8. LHL = {0.9}2-{0.1}2 = 0.8. DNE. • (D) For c = 0: RHL = tan(1)/1 = tan 1. LHL = tan(-1)/(-1) = tan 1. Limit exists.
Correct Answer: (B, C)