This quiz works best with JavaScript enabled. Home > Cbse > Class 11 > Science > Mathematics > Class 11 Mathematics Chapter 13 Limits And Derivatives – Quiz 3 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 11 Mathematics Chapter 13 Limits And Derivatives Quiz 3 (45 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Find an equation for the slope of the graph of y = 10x-2x$^{2}$. A) M = 10-4x. B) M = 10. C) M =-4x. D) M = 6x. Show Answer Correct Answer: A) M = 10-4x. 2. Find f'(x) if f(x)=x$^{2}$ A) 2x$^{2}$. B) X$^{2}$. C) 2. D) 2x. Show Answer Correct Answer: D) 2x. 3. Evaluate $\lim_{x\rightarrow9}\\frac{x-9}{\sqrt{x}-3}$ A) 1/6. B) 0. C) DNE. D) 6. Show Answer Correct Answer: D) 6. 4. $\lim_{x\rightarrow2}\left|\frac{x^3-2x^2}{x-5x+6}\right|$ A) -4. B) -1. C) 1. D) 4. Show Answer Correct Answer: A) -4. 5. Evaluate $\lim_{x\rightarrow2}\left(2x+3\right)$ A) 5. B) 7. C) 1. D) 0. Show Answer Correct Answer: B) 7. 6. The average rate of change is the same thing as A) The cost of a stamp. B) The derivative. C) Marginal cost. D) The slope between two points. Show Answer Correct Answer: D) The slope between two points. 7. Find the slope of the line tangent to the graph of y = x$^{3}$-3 at (-2, -11). A) 8. B) 9. C) 6. D) 12. Show Answer Correct Answer: D) 12. 8. Evaluate $\lim_{x\rightarrow1}\frac{x^2-1}{x-1}$ A) Does not exist. B) 0. C) -2. D) 2. Show Answer Correct Answer: D) 2. 9. What is the limit of h(x) as x approaches a, if h(x) = p(x)/q(x)? A) Q(a)/p(a). B) P(a)-q(a). C) P(a)/q(a). D) P(a)*q(a). Show Answer Correct Answer: C) P(a)/q(a). 10. Find the derivative of the given equationf(x) =-4x A) -4. B) 0. C) X. D) 4. Show Answer Correct Answer: A) -4. 11. Want is the equation of the tangent to $f\left(x\right)=3x^2-2x$ A) $y-8=10\left(x-2\right)$. B) Y-8=10(x-2) Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $y-8=10\left(x-2\right)$. 12. Evaluate $\lim_{x\rightarrow6}\frac{x^2-36}{x-6}$ A) 12. B) 6. C) 0. D) Undefined. Show Answer Correct Answer: A) 12. 13. Differentiate:f(x) = x$^{7}$ (5 + 8x)$^{3}$ A) F '(x) = x$^{2}$ (5 + 8x)$^{6}$ (35 + 80x). B) F '(x) = 8x$^{7}$ (5 + 8x)$^{2}$ (35 + 80x). C) F '(x) = x$^{6}$ (5 + 8x)$^{2}$ (35 + 80x). D) F '(x) = x$^{6}$ (5 + 8x)$^{3}$ (35 + 80x). Show Answer Correct Answer: C) F '(x) = x$^{6}$ (5 + 8x)$^{2}$ (35 + 80x). 14. What is the equation of the tangent line at x = 1 $of$ $f\left(x\right)=\\sqrt{x}$ A) $y=\frac{1}{2}x-\frac{1}{2}$. B) $y=\frac{1}{2}x+\frac{1}{2}$. C) $y=2x-1$. D) $y=2x$. Show Answer Correct Answer: B) $y=\frac{1}{2}x+\frac{1}{2}$. 15. Find h'(t) if h(t)=5x$^{3}$-2x A) 15x$^{2}$-2x. B) 3x$^{2}$. C) 15x$^{2}$-2. D) 15x$^{2}$. Show Answer Correct Answer: C) 15x$^{2}$-2. 16. The derivative of x$^{2}$ cos x is A) Cosx-x$^{2}$ sin x cos x. B) 2x sin x-x$^{2}$ sin x. C) 2x cos x-x$^{2}$ sin x. D) 2x sin x-x$^{2}$ cos x. Show Answer Correct Answer: C) 2x cos x-x$^{2}$ sin x. 17. Differentiate $f\left(x\right)=\frac{2}{x^5}-5$ A) $\frac{2}{x^6}$. B) $-\frac{10}{x^6}$. C) $-\frac{10}{x^4}$. D) $-\frac{5}{x^4}$. Show Answer Correct Answer: B) $-\frac{10}{x^6}$. 18. $Evaluate\\lim_{x\rightarrow0}\\frac{\sin^24x}{x^2}$ A) 14. B) 16. C) 12. D) 0. Show Answer Correct Answer: B) 16. 19. Find the slope of the tangent line to f(x) =-3x$^{2}$-6x at x = 1. A) F'(x) = 6x. B) M =-12. C) M = 0. D) F'(x) =-6x-6. Show Answer Correct Answer: B) M =-12. 20. What is the limit of g(x) / h(x) as x approaches a, if g(a) = p and h(a) = q? A) P / q. B) P + q. C) P * q. D) P-q. Show Answer Correct Answer: A) P / q. 21. When is a limit said to exist? A) When it is undefined. B) When it equals infinity. C) When it is a real number. D) When it is a complex number. Show Answer Correct Answer: C) When it is a real number. 22. $\lim_{x\rightarrow0}=\frac{\sqrt[]{x+4}-2}{x}$ A) 0.25. B) 0.50. C) 0.75. D) None of the above. Show Answer Correct Answer: A) 0.25. 23. Use a graph to find $\lim_{x\rightarrow0}\\frac{1-\cos x}{x}$ A) 0. B) -1/3. C) 1. D) -1. Show Answer Correct Answer: A) 0. 24. What is the notation for the derivative of a function f(x)? A) F(x). B) F'(x). C) F" (x). D) Df/dx. Show Answer Correct Answer: B) F'(x). 25. What happens if direct substitution in limit calculation yields an undefined value? A) The limit is infinity. B) The limit does not exist. C) The function is continuous. D) Another method must be used. Show Answer Correct Answer: D) Another method must be used. 26. What is the derivative of (uv) with respect to x? A) U'v + uv'. B) U-v. C) U/v + v/u. D) U'v-uv'. Show Answer Correct Answer: A) U'v + uv'. 27. If $f(x) = x^2$ $f'(x)$ A) $x$. B) $x^2$. C) $2x$. D) $2$. Show Answer Correct Answer: C) $2x$. 28. F'(x) = 3x+4. Find the slope of the line tangent to f(x) at the point (0, 7) A) 7. B) 3. C) 4. D) -7. Show Answer Correct Answer: C) 4. 29. Which of the following is an application of derivatives? A) Calculating the area under a curve. B) Solving quadratic equations. C) Factoring polynomials. D) Finding the maximum or minimum values of a function. Show Answer Correct Answer: D) Finding the maximum or minimum values of a function. 30. $Evaluate\\int_1^5x^3dx$ A) 41. B) 156.25. C) 156. D) 41.33. Show Answer Correct Answer: C) 156. 31. Find an equation for the slope of the graph of y = x$^{3}$-7 A) M = 7. B) M = 3x$^{2}$. C) M = 3x-7. D) M = 3x. Show Answer Correct Answer: B) M = 3x$^{2}$. 32. Differentiate 1/x$^{2}$ A) -2/x$^{3}$. B) 2x$^{-1}$. C) -2x$^{-1}$. D) 1/2x. Show Answer Correct Answer: A) -2/x$^{3}$. 33. Instantaneous rate of change means the same thing as A) Slope of a secant line. B) Slope of the normal line. C) Potato. D) Slope of the tangent line. Show Answer Correct Answer: D) Slope of the tangent line. 34. Evaluate $\lim_{x\rightarrow1}\\frac{3x^2-7x+4}{2x^2+3x-5}$ A) $-\frac{4}{5}$. B) $-\frac{1}{7}$. C) The limit does not exist. D) $\frac{3}{2}$. Show Answer Correct Answer: B) $-\frac{1}{7}$. 35. Find the derivative of f(x) = 5x$^{2}$ + 7x-3. A) 10x + 7. B) 2x + 4. C) 10x + 4. D) 2x + 7. Show Answer Correct Answer: A) 10x + 7. 36. What is the derivative of ax? A) X. B) 0. C) 1. D) A. Show Answer Correct Answer: D) A. 37. $Evaluate\\lim_{x\rightarrow0}\\frac{\left(1+x\right)^5-1}{\left(1+x\right)^2-1}$ A) 5. B) 1. C) 2. D) 3. Show Answer Correct Answer: D) 3. 38. Find the derivative of the given equationf(x) = x$^{4}$$^{ }$ A) X$^{4}$. B) 4x$^{3}$. C) 4x. D) X$^{3}$$^{ }$. Show Answer Correct Answer: B) 4x$^{3}$. 39. What is the derivative of a real valued function f at point a? A) F(a)-f(a-h)/h. B) F(a-h)/h. C) F(a+h)-f(a)/h. D) F(a+h)-f(a)*h. Show Answer Correct Answer: C) F(a+h)-f(a)/h. 40. Find the derivative of the given equation $x^3+x^2+12$ A) $x^2+x$. B) $3x^2+2x$. C) $3x^3+2x^2$. D) $5x$. Show Answer Correct Answer: B) $3x^2+2x$. 41. What is the derivative of x$^{n}$? A) (n-1)x$^{n}$. B) Nx$^{n-1}$. C) Nx$^{n+1}$. D) (n+1)x$^{n-1}$. Show Answer Correct Answer: B) Nx$^{n-1}$. 42. What is the limit $\lim_{x \to 3} (x^2-9)$ A) 3. B) 6. C) 9. D) 0. Show Answer Correct Answer: D) 0. 43. $\lim_{x+2\rightarrow0}\\frac{8x^2+14x-4}{2\left(x+2\right)}= ..... $ A) $0$. B) $-9$. C) $10$. D) $7$. E) $-7$. Show Answer Correct Answer: B) $-9$. 44. $\lim_{x\rightarrow\frac{1}{2}}=\frac{x^{-1}-2}{x-\frac{1}{2}}$ A) -2. B) 4. C) 2. D) -4. Show Answer Correct Answer: D) -4. 45. To find the derivative of f(x) = xe$^{x }$you should use: A) The chain rule. B) The product rule. C) The quotient rule. D) The power rule combined with the chain rule. Show Answer Correct Answer: B) The product rule. ← PreviousRelated QuizzesScience QuizzesClass 11 QuizzesClass 11 Mathematics Chapter 13 Limits And Derivatives Quiz 1Class 11 Mathematics Chapter 13 Limits And Derivatives Quiz 2Class 11 Mathematics Chapter 1 Sets QuizClass 11 Mathematics Chapter 10 Straight Lines QuizClass 11 Mathematics Chapter 11 Conic Sections QuizClass 11 Mathematics Chapter 12 Introduction To Three Dimensional Geometry QuizClass 11 Mathematics Chapter 14 Mathematical Reasoning QuizClass 11 Mathematics Chapter 15 Statistics Quiz 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books