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Class 12 Mathematics Chapter 5 Continuity And Differentiability Quiz 2 (25 MCQs)

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1. Define continuity of a function at a point.
2. If y=log x then $\frac{d^2y}{dx^2}$
3. Find $\frac{dy}{dx}$ $y=x^2e^x$
4. Let f(x) = 1 for x <=-1f(x) = |x|, -1 < x < 1f(x) = 0 for x >= 1
5. Leibnitz rule
6. A function whose graph is otherwise continuous will fail to have a derivative at a point where the graph has a .....
7. The composition of two continuous functions is a continuous function.
8. Which of these is NOT a hypothesis of the Mean Value Theorem (MVT)?
9. What is the relationship between differentiability and continuity?
10. Which theorem states that the sum, difference, product, and quotient of continuous functions are continuous?
11. At what point is $f\left(x\right)=\frac{x^2-25}{x-5}$
12. All functions below are continuous and differentiable EXCEPT ONE. Which is it?
13. If a function is differentiable, it is also continuous.
14. Derivative of cos$^{-1}$(2x)
15. On what value/s of X will make the function $f\left(x\right)=x-4$
16. The function f(x) = x$^{2}$-2x+1 is continuous and differentiable at all real values of x.
17. Which of the following is a property of logarithmic functions?
18. Rolle's theorem is applicable for the function f (x) = |x-1| in [0, 2].
19. The function m(x) = |2x-3| is
20. The funciton f(x) = x$^{2}$-2x+1, continuous to the interval [-7, 7]
21. The function $f\left(x\right)=\frac{5}{x+2}$
22. Explain the concept of a piecewise function.
23. If Limit exist in a function it always unique
24. Find dy/dx if y$^{4}$ = x
25. Which of the following statements is true regarding the continuity of a function?
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