Question:
Find left, right and limit at x = 0 f(x) = 1, when x is less than or equal to 0, f(x) = 2 when x is greater than 0. Here they have said that x value is equal to zero. So why do we need to take x greater than or equal or less than zero.
Answer:
Given f(x) = 1; x ≤ 0
= 2, x > 0
Now, value of the function at x = 0 is
f(0) = 1 {since x ≤ 0}
LHL:
limx -> 0- f(x)
= limh -> 0 f(0 - h)
= limh -> 0 (1)
= 1
RHL:
limx -> 0+ f(x)
= limh -> 0 f(0 + h)
= limh -> 0 (2)
= 2
Here, we take x ≤ 0 for the calculation of LHL and x > 0 for the calculation of RHL.
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