Continuity And Differentiability — Mathematics

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Question 1

EasyJEE

A function f is continuous at x=a if:

lim_{x→a} f(x) = f(a)

f(a) exists

lim_{x→a} f(x) exists

All of these

Question 2

EasyJEE

The function f(x)=|x| is continuous at x=0 but not differentiable because:

LHD and RHD are different

Derivative is infinite

f(0) is not defined

Function is not continuous

Question 3

EasyJEE

If a function is differentiable at a point, then it is:

Always continuous

Not necessarily continuous

Always discontinuous

Monotonic

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