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# NCERT Solutions Class 12 Maths Continuity and Differentiability

Hi Students, Welcome to Amans Maths Blogs (AMB). In this post, you will get the NCERT Solutions for Class 12 Maths Continuity and Differentiability Miscellaneous Exercise.

CBSE Class 12th is an important school class in your life as you take some serious decision about your career. And out of all subjects, Maths is an important and core subjects. So CBSE NCERT Solutions for Class 12th Maths is major role in your exam preparation as it has detailed chapter wise solutions for all exercise. This NCERT Solutions can be downloaded in PDF file. The downloading link is given at last.

NCERT Solutions for Class 12 Maths are not only the solutions of Maths exercise but it builds your foundation of other important subjects. Getting knowledge of depth concept of CBSE Class 12th Maths like Algebra, Calculus, Trigonometry, Coordinate Geometry help you to understand the concept of Physics and Physical Chemistry.

As we know that all the schools affiliated from CBSE follow the NCERT books for all subjects. You can check the CBSE NCERT Syllabus. Thus, NCERT Solutions helps the students to solve the exercise questions as given in NCERT Books.

## NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise

Differentiate w.r.t. x the function in Exercises 1 to 11.

NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 1.

(3x2 – 9x + 5)9

NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 2.

sin3 x + cos6 x

NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 3.

(5x)3 cos 2x

NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 4.

sin–1(x√x), 0 ≤ x ≤ 1

NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 5. NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 6. NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 7.

(log x)log x, x > 1

NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 8.

cos (a cos x + b sin x), for some constant a and b.

NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 9.

(sin x – cos x)(sin x – cos x), π/4 < x < 3π/4

NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 10.

xx + xa + ax + aa, for some fixed a > 0 and x > 0

NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 11. NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 12.

Find dy/dx, if y = 12 (1 – cos t), x = 10 (t – sin t), -π/2 < t < π/2.

NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 13.

Find dy/dx, if y = sin–1 x + sin–1 √(1 – x2), -1 ≤ x ≤ 1.

NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 14.

If x√(1 + y) + y√(1 + x) = 0, for -1 < x < 1, prove that dy/dx = -1/(1 + x)2.

NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 15.

If (x – a)2 + (y – b)2 = c2, for some c > 0, prove that is a constant independent of a and b.

NCERT Solutions:  NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 16.

If cos y = x cos (a + y), with cos a ≠ ± 1, prove that .

NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 17.

If x = a (cos t + t sin t) and y = a (sin t – t cos t), find d2y/dx2.

NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 18.

If f (x) = | x |3, show that f ″(x) exists for all real x and find it.

NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 19.

Using mathematical induction prove that for all positive integers n.

NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 20.

Using the fact that sin (A + B) = sin A cos B + cos A sin B and the differentiation, obtain the sum formula for cosines.

NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 21.

Does there exist a function which is continuous everywhere but not differentiable at exactly two points? Justify your answer.

NCERT Solutions:  NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 22. NCERT Solutions: NCERT Solutions Class 12 Maths Continuity and Differentiability Miscellaneous Exercise: Ques No 23.

If – 1 ≤ x ≤ 1, show that .

NCERT Solutions: 