If is differentiable at , then consider the following statements: I. is continuous at II. Which of the statements given above is/are correct? यदि , पर अवकलनीय है , तो निम्नलिखित कथनों पर विचार कीजिए: I. , पर संतत है II. उपर्युक्त कथनों में से कौन-सा/कौन-से सही है/हैं ?

Both I and II Explanation: The correct answer is (c) Both I and II . The Mathematical Reasoning: Differentiability implies Continuity: A core theorem in calculus states that if a function is differentiable at a point , then it must be continuous at that point. Definition of Continuity: By definition, a function is continuous at if and only if: Since Statement I asserts that is continuous at , and Statement II provides the formal definition of that continuity, both statements are mathematically equivalent and both are true.

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NDA 2026 — Mathematics PYQ

NDA | Mathematics | 2026

If $f (x)$ is differentiable at $x = a$ , then consider the following statements:

I. $f (x)$ is continuous at $x = a$

II. $lim_{x \to a} f (x) = f (a)$

Which of the statements given above is/are correct?

यदि $f (x)$ , $x = a$ पर अवकलनीय है, तो निम्नलिखित कथनों पर विचार कीजिए:

I. $f (x)$ , $x = a$ पर संतत है

II. $lim_{x \to a} f (x) = f (a)$

उपर्युक्त कथनों में से कौन-सा/कौन-से सही है/हैं ?

Choose the correct answer: