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Free CBSE - Class 12 Mathematics - Continuity and Differentiability worksheets

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Here is a Sample Worksheet for you to Practice. Download this worksheet to see the answers.

1.
If $y = Ae^{mx} + Be^{nx}$, show that $\frac{d^2y}{dx^2} - (m + n)\frac{dy}{dx} + mny = 0$
2.
If $y = 500e^{7x} + 600e^{-7x}$, show that $\frac{d^2y}{dx^2} = 49y$
3.
If $e^y (x + 1) = 1$, show that $\frac{d^2y}{dx^2} = \left(\frac{dy}{dx}\right)^2$
4.
If $y = (\tan^{-1} x)^2$, show that $(x^2 + 1)^2 y_2 + 2x(x^2 + 1)y_1 = 2$
5.

Find the second order derivatives of the functions. $\tan^{-1} x$

6.

Find the second order derivatives of the functions. $\log(\log x)$

7.

Find the second order derivatives of the functions. $\sin(\log x)$

8.
If $y = 5 \cos x - 3 \sin x$, prove that $\frac{d^2y}{dx^2} + y = 0$
9.
If $y = \cos^{-1} x$, Find $\frac{d^2y}{dx^2}$ in terms of $y$ alone.
10.
If $y = 3 \cos(\log x) + 4 \sin(\log x)$, show that $x^2 y_2 + xy_1 + y = 0$
- OR -

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Top Tutors who teach CBSE - Class 12 Mathematics Continuity and Differentiability

Saurav Continuity and Differentiability in Mumbai
(25)
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locationImg Nerul, Mumbai
10 yrs of Exp students 5 students
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rsIcon 500 per hour
M.SC MATHS from JAMIA MILLIA ISLAMIA, NEW DELHI, 10+Years of Teaching Experience.
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Jordan John

An Excellent Maths Tutor! I am truly grateful to have found such a dedicated and exceptional Maths tutor like Sir Saurav. Sir has a remarkable ability to explain even challenging concepts with clarity and patience. He covers every type of question, provides thought-provoking challenges, and ensures that we genuinely understanding everything excellently. What makes his teaching truly special is his personal attention and genuine concern for his students. He patiently clears every doubt, gives us his complete time and attention, and constantly checks whether we have understood before moving forward. His strong conceptual knowledge, encouraging approach, and commitment to his students make learning Maths both meaningful and enjoyable. This is my first experience learning from him, and I can confidently say that I would highly recommend him to anyone looking for a knowledgeable, caring, and truly outstanding Maths tutor. He goes far beyond teaching the subject he inspires confidence and makes his students believe they can master it.

Skills: Mathematics

(69)
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locationImg Sector 92, Gurgaon
20 yrs of Exp students 2 students
1392 hrs of classes completed
rsIcon 1200 per hour
Teaching mathematics since last 20 years. Doing research on Vedic mathematics
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Ramu Nutakki

Very patient. Makes learning fun and productive. A seasoned and competent teacher. Makes a subject as mind-bogging as Math very easy to understand. Awesome experience!

Skills: Mathematics , Physics and more

Ashish Bhatia Continuity and Differentiability in Surat
(63)
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locationImg Jahangirpura, Surat
15 yrs of Exp students 6 students
3744 hrs of classes completed
rsIcon 250 per hour
Top Tutor on Urban Pro | Maths & Sci Educator | IB, ICSE, IGCSE, CBSE | 17+ yrs Exp. | 1600 + hrs
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Emma

Sir explains every concept very clearly and makes sure that i understand each and every point. He teaches slowly and patiently, which makes it easy to follow the class. He also clears my doubts using simple and basic words, so even difficult concepts become easier to understand. His way of teaching helps me build a strong understanding of Science.

Skills: Mathematics

(26)
Top Tutor
locationImg Mahavir Enclave, Delhi
20 yrs of Exp students 9 students
1019 hrs of classes completed
rsIcon 800 per hour
Ex Maths faculty Career point (Kota) & Aakash Institute. 20+ years of IITJEE Coaching Experience
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Vedant Singh Parmar

Honestly, this has been the most amazing maths class for 12th CBSE and JEE prep! The way concepts like calculus, integration, and coordinate geometry are explained makes everything so easy to understand. The teacher breaks down even the toughest JEE problems step by step — no confusion at all! Practice sheets are super helpful, and doubts get cleared instantly. Board exam syllabus and JEE Advanced topics are both covered brilliantly without feeling overwhelming. My confidence has shot up so much! If you're a 12th student aiming to crack JEE, this class is absolutely a game-changer. Highly recommended!

Skills: Mathematics

Top Concept Videos in Mathematics Continuity and Differentiability

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The Magical Tools of Advanced Differentiation

CBSE - Class 12>Mathematics>Continuity and Differentiability

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