how to find out continuity and differentiability?
how to find out continuity and differentiability?
MAlav Shah , 10 Years ago
Grade 12
Differential Calculus> how to find out continuity and differenti...
1 Answers
Jitender Singh
Last Activity: 10 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)]
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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