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Class 11 Mathematics Chapter 13 Limits And Derivatives Quiz 2 (25 MCQs)

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1. Differentiate y = (x$^{3 }$-1)$^{100}$
2. D/dx cos x =
3. Find the derivative of:$f\left(x\right)=4\sqrt{x}$
4. Find the derivative. f(x) =-8x$^{-3}$ + 5x
5. Evaluate $\lim_{x\rightarrow-1}\frac{x^4-1}{x+1}$
6. Evaluate $\lim_{x\rightarrow-4}\\frac{3x^2+11x-4}{x^2+3x-4}$
7. Find the slope at x = 3 of the equation f(x) = 3x$^{2}$
8. Find the vertical asymptote(s) (if any) of the graph of the function. 3x / (x$^{2}$ + 9)
9. Find $\lim_{x\rightarrow\infty}\\frac{2x^2}{x+1}$
10. $f\left(x\right)=10x^{-4}-5x^{-2}+x+1$
11. Approximate the instantaneous rate of change of the function at x =-1. $f\left(x\right)=3x^2+2x-1$
12. $Evaluate\\lim_{x\rightarrow1}\\frac{x^{15}-1}{x^{10}-1}$
13. Find the derivative of the given functionf(x) = x$^{4}$ + 4x$^{3 }$-2x$^{2}$
14. If $\lim_{x\rightarrow c}f\left(x\right)=-\infty$ $\lim_{x\rightarrow c}g\left(x\right)=+\infty$ $\lim_{x\rightarrow c}\left[f\left(x\right)+g\left(x\right)\right]=0$
15. Determine the derivative of f(x) = 6x
16. Write the slope of the line tangent to the graph of y=x$^{2}$-2 at the point x =-8.
17. If $f\left(x\right)$ $\lim_{x\rightarrow c}f\left(x\right)$
18. The equation of motion of a particle is s = 2t$^{3 }$-5t$^{2 }$+ 3t + 4, which is the function of its acceleration?
19. Evaluate $\lim_{x\rightarrow+\infty}\\frac{-4}{3-x^2}$
20. Find the derivative of the given equationf(x) = $\frac{1}{x^2}$
21. Differentiate h(x) = 3x$^{5/3}$-6x$^{1/6}$ + 3x
22. Evaluate $\lim_{x\rightarrow0}\frac{x^2+x}{x^2-3x}$
23. What is the value of the limit $\lim_{x \to 2} (3x + 1)$
24. Given that $y=\frac{x+2}{x-3}$
25. $\lim_{x\rightarrow1}\\frac{x^3-3x^2+2x}{x^3-4x^2+3x}= ..... $
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