Maths · Calculus · chapter 12 of 14
Class 11 Maths Chapter 12: Limits and Derivatives Assertion-reason questions with answers
2 assertion-reason questions on Limits and Derivatives, each with its answer and the reason, written from the NCERT chapter. For school exams on the CBSE pattern 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): \limx→0 sin xx = 1. Reason (R): For 0 < |x| < π/2, cos x < sin xx < 1, and \limx→0 cos x = 1.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.
Both are true. (sin x)/x is sandwiched between cos x and the constant 1, both of which tend to 1, so by the Sandwich Theorem the limit is 1: R is exactly the reason for A.
Question 2
Assertion (A): The derivative of x4 is 4x3. Reason (R): For every positive integer n and real a, \limx→a xn = an.
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Answer: (b) Both A and R are true, but R is not the correct explanation of A.
A is Theorem 6 with n = 4; R is the limit of a power, also true. R is about the value a power tends to, not about its rate of change, so it does not explain A.
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