Question

A function /is said to be continuous for x ∈ R, if (a) it is continuous at x = 0 (b) differentiable at x = 0 (c) continuous at two points (d) differentiable for x ∈ R​

Answer 1

Answer:

answer is in the attachment

Step-by-step explanation:

hope it helps you

Answer 2

Option D is the correct answer.

A Function is said to be continuous for all x belonging to r in the interval [a,b] only when:

• The function is continuous in the interval [a,b].
• The function must be differentiable in the interval (a,b).
• There must be no discontinuities at any point in the closed interval [a,b].

• If the function is continuous at x=0 it can be discontinuous at other values of x. Hence, this statement is incorrect.
• If the function is differentiable at x=0, it implies the function is continuous only at x=0 but not at the other values of x. Hence, this statement is incorrect.
• If a function is continuous at two points, it may or may not be continuous at further points. Hence, the given statement is incorrect.
• For a function to be continuous in an interval, it must be differentiable at every point in the open interval. Hence, this statement is the correct answer.

Therefore, Option D is the correct answer.