Question

What is the answer with a thorough explanation of each option please

Answer 1

Condition I

If f is defined at x=a, then,

`\lim _(x\rightarrow a)f(x)=f(a)`

The above is true but it is not true for a stepwise function

Condition II

If f is continuous at x=a, then

`\lim _(x\rightarrow a)f(x)=f(a)`

The second statement above is true for it meets the condition for continuity of a limiting function

Condition III

If f is differentiable at x=a, then

`\lim _(x\rightarrow a)f(x)=f(a)`

The third statement above is also true for a limiting function of differentiation.

Hence, statements II and III are true, OPTION D