The CBSE has announced Class 12th Mathematics Examination 2020. The students who will be appearing for the CBSE Class 12th Examination 2020 can go through the list of important questions and answers for chapter 5 - Continuity and Differentiability. These are based on the latest CBSE syllabus.
Question 1- Examine the continuity of the function f (x) = x3 + 2x2 - 1 at x = 1.
Answer: Thus, f(x) is continuous at x = 1.
Question 2- Prove that the function f remains discontinuous at x = 0, regardless of the choice of k.
Answer:
Question 3- Find the values of p and q, so that the given equation is differentiable at x = 1.
Answer: p = 3 and q = 5
Question 4-
Answer:
Question 5- Find a point on the curve y = (x - 3)2, where the tangent is parallel to the chord joining the points (3, 0) and (4, 1).
Answer: (7/2, 1/4)
Question 6- f(x) = |x| + |x – 1| at x = 1.
Answer: LHL = RHL = f(1)
Question 7- Find the values of a and b such that the function f defined by
Answer: b = - 1 and a = 1
Question 8- Find the points of discontinuity of the composite function y = f{f(x)}.
Answer: y is discontinuous at x = -5/2.
Question 9- Examine the differentiability of f, where f is defined by
Answer: f(x) is not differentiable at x = 2.
Question 10- Show that the function f(x) = |sin x + cos X|is continuous at x = π.
Answer: Since g(x) and h(x) are continuous functions and f(x)is a composite function. We know that composite functions of two continuous functions are also a continuous function. Hence, f(x) = |sin x + cos X| is a continuous function everywhere.
The students will find the above-mentioned questions helpful for the last minute preparation for CBSE Class 12th Mathematics Examination 2020. These important questions are based on the NCERT textbook, previous year papers and sample papers. The students can also check the links mentioned below:
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