Maths · Calculus · chapter 5 of 13

Class 12 Maths Chapter 5: Continuity and Differentiability Assertion-reason questions with answers

2 assertion-reason questions on Continuity and Differentiability, each with its answer and the reason, written from the NCERT chapter. For the CBSE board and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter. Each question gives an Assertion (A) and a Reason (R); choose how they stand to each other.

Question 1
Assertion (A): f(x) = x3 − 4x + 7 is continuous at x = 2. Reason (R): Every polynomial function is continuous.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

f is a polynomial, and a polynomial is continuous at every real number: lim_(x→2) f(x) = 8 − 8 + 7 = 7 = f(2). R is true and is the reason A holds.

Question 2
Assertion (A): f(x) = |x − 3| is continuous at x = 3. Reason (R): A function that is continuous at a point is differentiable at that point.
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Answer: (c) A is true, but R is false.

Both one-sided limits of |x − 3| at 3 are 0 = f(3), so A is true. R is the converse of Theorem 3 and is false: |x − 3| itself has left hand derivative −1 and right hand derivative 1 at 3.

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