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Class 12 Mathematics: Continuity and Differentiability
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MCQs on continuity, differentiability, exponential and logarithmic functions, logarithmic differentiation, functions derivatives in parametric forms, second order derivatives and mean value theorem.

Class 12 Mathematics: Continuity and Differentiability
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25 Questions

1. What are the kinds of discontinuity?
2. Find the second order derivative if y=e2x2.
3. What is derivative of xn?
4. What is the relation between f(a) and f(b) according to Rolle's theorem?
5. Value after differentiating cos (x2+5) is ________
6. What is the mathematical expression for the definition of continuity?
7. Differentiate 8e-x+2ex w.r.t x.
8. Differentiate 7x(2e2x) with respect to x.
9. Differentiate 8ecos2x w.r.t x.
10. Find the second order derivative y=e2x+sin-1⁡ex .
11. If y=log⁡(2x3), find \(\frac{d^2 y}{dx^2}\).
12. Differentiate \(\sqrt{\frac{x+1}{3x-1}}\) with respect to x.
13. Find \(\frac{d^2y}{dx^2}\), if y=tan2⁡x+3 tan⁡x.
14. Function f should be _____ on [a,b] according to Rolle's theorem.
15. Rolle's theorem is a special case of _____
16. Find \(\frac{dy}{dx}\) of 2x+3y = sinx.
17. Differentiate 2(tan⁡x)cot⁡x with respect to x.
18. Differentiate 3 sin-1⁡(e2x) w.r.t x.
19. Differentiate 4xex with respect to x.
20. What is derivative of cotx?
21. Differentiate 7 log⁡(x4.5ex3) w.r.t x.
22. Is f(x) = \( \begin{cases}
\frac {sin2x}{x} & if \, x \neq 0 \\
1 & if \, x = 0 \\
\end{cases} \) a continuous function?
23. Find \(\frac{dy}{dx}\), if x=2et and y=log⁡t
24. What is the mathematical expression for f is left continuous on (a,b)?
25. Find \(\frac{dy}{dx}\), if x=log⁡t2 and y=\(\frac{1}{t}\).

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