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Class 12 Mathematics Chapter 5 Continuity And Differentiability Quiz 3 (25 MCQs)

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1. Can a function be continuous but not differentiable?
2. Every Differentialable function are continuous but converse is not true
3. For a function, $f\left(x\right)$ $x=c$ $\lim_{x\rightarrow c}f\left(x\right)$ $f\left(c\right)$ $\lim_{x\rightarrow c}f\left(x\right)=f\left(c\right)$
4. If (a, b) is a local maximum, then what will be true about f'(a)?
5. If $f\left(x\right)$
6. What is the significance of the derivative of a function?
7. |sin x| is a differentiable function for every value of x.
8. The function $f\left(x\right)=\frac{5}{x^4-16}$
9. What is the definition of continuity at a point c for a function f?
10. Identify the point(s) of discontinuity. $f\left(x\right)=\frac{x-1}{3x^2-3}$
11. A function is continuous at a number c if and only if $f\left(c\right)=\lim_{x\rightarrow c}f\left(x\right)$
12. The function f (x) = |x| + |x-1| is
13. The function f(x) = sin ( $\pi$ $\pi$
14. The number of points at which the function f (x) = $\frac{1}{x-\left[x\right]}$
15. Cos |x| is differentiable everywhere.
16. If a function is differentiable at x=c, can it be discontinuous at x=c?
17. Find the second derivative of the given equationf(x) = 1-x$^{2}$
18. If f(2)=3 and f'(2)=-1, then the equation of the tangent line to f(x) at x = 2 is
19. F(x) = 5x-4 ; 0 < x <= 1& f(x) = 4x$^{2}$ + 3ax ; 1 < x < 2 is continuous for all x $\in$
20. Determine any point(s) of discontinuity for the following function. $f\left(x\right)=\frac{3x-6}{x^2-9x+14}$
21. What is the limit of the function f(x) = 1/x as x approaches 0?
22. The number of points of discontinuinity of the function f(x) = $\frac{x^2-3x+2}{4x-x^3}$
23. If f . g is continuous at x = a, then f and g are separately continuous at x = a.
24. If f is continuous on its domain D, then | f | is also continuous on D.
25. The derivative of log ( cosec x-cot x) with respect to x is
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