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Class 11 Mathematics Chapter 13 Limits And Derivatives Quiz 1 (25 MCQs)

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1. Find the average rate of change of f(x)=2x$^{2}$+3x-1 from 1 to 2.
2. $\lim_{t\rightarrow0}\\frac{\frac{1}{x+t}-\frac{1}{x}}{t}= ..... $
3. What is the derivative of f(x) =-2/x
4. Find the derivative f(x) = tanxcosx
5. Evaluate $\lim_{x\rightarrow0}-3$
6. What is the derivative of tan(x)?
7. If y = (sin x + cos x)/(sin x-cos x), dy/dx at x = 0 is
8. Evaluate $\lim_{x\rightarrow6}\\frac{x^2-6x}{x^2-7x+6}$
9. $\frac{d}{dx}\left(\sqrt[]{x}\right)$
10. $Evaluate\\lim_{x\rightarrow0}\left[\operatorname{cosec}x-\cot x\right]$
11. Find the derivative of the given equationf(s) = 12-8s
12. FInd the derivative:f(x) = (-2/3)x$^{3}$-(1/2)x$^{2}$ + 9x
13. The first principles definition of the derivative of f(x) is $f'\left(x\right)=\lim_{h\longrightarrow0}\\frac{4\left(x+h\right)^3-4x^3}{h}$
14. Find dy/dx by Implicit Differentiation2xy$^{3 }$-x$^{2}$y = 2
15. Find the derivative of f(x) = (x$^{6}$ + 4)$^{5}$
16. Find an equation of the tangent line to the graph of f(x) at the point (1, 100)f(x) = (5x$^{5}$ + 5)$^{2}$
17. What is the equation of the line tangent to f(x)=x$^{4}$-2x at the point x=-1?
18. What is the meaning of a discontinuity at point A in a function?
19. Differentiate f(x) = 5x$^{7}$.
20. What does continuity in a function imply?
21. Use a graph to estimate $\lim_{x\rightarrow-2}\left(4x^2+3x-1\right)$
22. Differentiate y= x$^{3}$ + 2x
23. $f\left(x\right)=x^{-6}$ $f'\left(x\right)$
24. $\lim_{x\rightarrow0}\\frac{\sin3x}{5x}$
25. Find the derivative of the given equationf(x) = x$^{4}$ + 4x$^{3 }$-2x$^{2}$
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