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how to find out continuity and differentiability?

how to find out continuity and differentiability?

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Ans:
Hello Student,
Please find answer to your question below

Continuity:
For a function f(x) to be continuous at any point x = a, limit of f(x) should exist at x = a
Limit hand limit & right hand limit should exist & equal & both of them should be equal to f(a).
Mathematically,
lim(x → a-) f(x) = f(a) = lim(x –> a+)

Differentiability:
For o function to be differentiable at any point x, left hand derivative & right hand derivative should exist & equal to each other.
Mathematically,
lim(h → 0) [(f(x+h)-f(x))/h] = lim(h → 0)[((f(x-h)-f(x))/-h)]



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