CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
A courier firm charges ₹50 for a parcel weighing up to 1 kg, and ₹80 for any parcel weighing more than 1 kg but up to 2 kg. If C(w) is the charge for weight w kg (0 < w ≤ 2), which statement is correct?
C has a jump discontinuity at w = 1. The charge approaches ₹50 from below 1 kg but ₹80 from above 1 kg. Since the left-hand and right-hand limits differ, the limit does not exist and the function cannot be continuous at that point.
- AC is continuous at w = 1
- BC has a jump discontinuity at w = 1Correct
- CC is discontinuous at w = 1.5
- DC has a limit of 65 at w = 1
Explanation
As w approaches 1 from the left, C = 50. As w approaches 1 from the right, C = 80. The left and right limits are unequal, so the limit does not exist and C has a jump discontinuity at w = 1. At w = 1.5 the charge is constant at 80, so it is continuous there.
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