This quiz works best with JavaScript enabled. Home > Cbse > Class 11 > Science > Mathematics > Class 11 Mathematics Chapter 13 Limits And Derivatives – Quiz 2 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 11 Mathematics Chapter 13 Limits And Derivatives Quiz 2 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. What does the limit of a function f(x) approaching L as x approaches x0 signify? A) F(x) is always continuous. B) F(x) is defined at x0. C) F(x) must be a polynomial. D) F(x) approaches L. Show Answer Correct Answer: D) F(x) approaches L. 2. $\lim_{x\rightarrow-4}\\frac{x^3+64}{x+4}$ A) 48. B) 16. C) DNE. D) $-\infty$. Show Answer Correct Answer: A) 48. 3. Find the derivative of the function f (x) = 2x$^{4}$-3x$^{3}$-7x$^{2}$ + 3x-7. A) F ' (x) = 8x$^{4}$-9x$^{3}$-14x$^{2}$ +3x. B) F ' (x) = 4x$^{3}$-3x$^{2}$-2x +1. C) F ' (x) = 8x$^{3}$-9x$^{2}$-14x +3. D) F ' (x) = 2x$^{3}$-3x$^{2}$-7x +3. Show Answer Correct Answer: C) F ' (x) = 8x$^{3}$-9x$^{2}$-14x +3. 4. If the first derivative of a function is zero at a given value of x, then the tangent line at that point is horizontal. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 5. What is the derivative of g(x) = 4x$^{3}$ A) 4. B) 12. C) 3. D) 12x$^{2}$. Show Answer Correct Answer: D) 12x$^{2}$. 6. Which of the following is the best description of a derivative? A) The y-intercept of a function. B) The area under a curve. C) The maximum value of a function. D) The slope of the tangent line at a point. Show Answer Correct Answer: D) The slope of the tangent line at a point. 7. What is the derivative of f at point a? A) F'(a) = lim(h$\rightarrow$0) (f(a)-f(a-h)) / h. B) F'(a) = lim(h$\rightarrow$0) (f(a)-f(a + h)) / h. C) F'(a) = lim(h$\rightarrow$0) (f(a + h)-f(a)) / h. D) F'(a) = lim(h$\rightarrow$0) (f(a + h) + f(a)) / h. Show Answer Correct Answer: C) F'(a) = lim(h$\rightarrow$0) (f(a + h)-f(a)) / h. 8. Evaluate $\lim_{x\rightarrow\infty}\-\frac{3x^3}{2x^2-2}$ A) The limit does not exist. B) $-\infty$. C) $-\frac{3x}{2}$. D) $\infty$. Show Answer Correct Answer: A) The limit does not exist. 9. Find dy/dx for y = 4x$^{3 }$+ 3x + 1 A) Dy/dx = 4x$^{2}$ + 3. B) Dy/dx = 12x$^{2}$ + 3x. C) Dy/dx = 4x$^{2}$ + 3x. D) Dy/dx = 12x$^{2}$ + 3. Show Answer Correct Answer: D) Dy/dx = 12x$^{2}$ + 3. 10. $\lim_{x\rightarrow3}\\frac{x^2-9}{x^2-5x+6}= ..... $ A) $-6$. B) $6$. C) $0$. D) $3$. E) $-3$. Show Answer Correct Answer: B) $6$. 11. Y=5x$^{2}$+ 3x + 9dy/dx = $_{}$ A) 10x+3. B) 10x. C) 10. D) 10x$^{2}$+3. Show Answer Correct Answer: A) 10x+3. 12. Find the fully simplified Derivative of y = 4x$^{2}$ + 3x + 6x$^{-2}$ A) Y' = 8x + 3-12x$^{-3}$. B) Y' = 8x + 3-12/x$^{3}$. C) Y' = 8x + 3 +12/x$^{3}$. D) Y' = 8x + 3 + 12/x. Show Answer Correct Answer: B) Y' = 8x + 3-12/x$^{3}$. 13. FInd the derivative:$f\left(x\right)=-\frac{2}{3}x^3-\frac{1}{2}x^2+9x$ A) $2x^2-x+9$. B) $-2x^2-x+9$. C) $2x^2-x-9$. D) $-2x^2+x+9$. Show Answer Correct Answer: B) $-2x^2-x+9$. 14. The position of an object in feet after t seconds is given by $s\left(t\right)=16t^2-\frac{1}{2}t^3$ A) 408 ft/s. B) 60 ft/s. C) 468 ft/s. D) 98 ft/s. Show Answer Correct Answer: D) 98 ft/s. 15. If $f\left(x\right)=-3x^2+6x-4$ $f'\left(x\right).$ A) $-3x+6$. B) $-6x+2$. C) $-6x+6$. D) $-6x^2+6$. Show Answer Correct Answer: C) $-6x+6$. 16. What is the equation of the tangent to the curve f(x)= 4x$^{2}$+2x-1 at the point x=0? A) Y=2x+2. B) Y = 2x-1. C) Y = 2x-3. D) Y+1=2(x+1). Show Answer Correct Answer: B) Y = 2x-1. 17. Find the derivative of the given equation $f\left(x\right)=4x$ A) -4. B) 4. C) X. D) 0. Show Answer Correct Answer: B) 4. 18. Find f'(x) for the function, then find f'(x) for the given x.-f(x) = 5x + 9, f'(2) A) F'(x) = 5x; f'(2) = 5. B) F'(x) = 5x; f'(2) = 10. C) F'(x) = 5; f'(2) = 5. D) F'(x) = 5; f'(2) = 10. Show Answer Correct Answer: C) F'(x) = 5; f'(2) = 5. 19. Find the antiderivative of f(x) = x$^{3}$-2x$^{2}$ + 4x-5. A) $f\left(x\right)=x^4+\frac{1}{3}x^3+2x^2-\frac{5}{2}x+C$. B) $f\left(x\right)=\frac{1}{4}x^4-\frac{2}{3}x^3+2x^2-5x+C$. C) $f\left(x\right)=\frac{1}{4}x^4-\frac{2}{3}x^3+2x^2+4x$. D) $f\left(x\right)=3x^2-4x+4$. Show Answer Correct Answer: B) $f\left(x\right)=\frac{1}{4}x^4-\frac{2}{3}x^3+2x^2-5x+C$. 20. If a function has a derivative that is negative, what does that tell you? A) The function is increasing. B) The function is decreasing. C) All the above. D) None of the above. Show Answer Correct Answer: B) The function is decreasing. 21. $\lim_{x\rightarrow\infty}\\frac{1-2x+2x^3}{x^3+x+1}=\ ..... $ A) -2. B) 1. C) -4. D) $\infty$. E) 2. Show Answer Correct Answer: E) 2. 22. Find dy/dx by Implicit Differentiation x$^{3}$ +y$^{3}$$^{ }$ = 36 A) 6-x. B) 0. C) -x$^{2}$/y$^{2}$. D) 3x$^{2}$ +3y$^{2}$. Show Answer Correct Answer: C) -x$^{2}$/y$^{2}$. 23. Which of the following statements is true about the limit $\lim_{x \to a} f(x)$ A) The limit may exist even if $f(a)$. B) The limit never exists if $f(a)$. C) The limit is always infinite. D) The limit always equals $f(a)$. Show Answer Correct Answer: A) The limit may exist even if $f(a)$. 24. If the graph of a function has a sharp corner at $x = 2$ $x = 2$ A) The derivative exists and is zero. B) The derivative does not exist. C) The derivative is positive. D) The derivative is negative. Show Answer Correct Answer: B) The derivative does not exist. 25. A farmer wants to construct a rectangular pigpen using 400 ft of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area? A) 102ft x 196 ft. B) 50 ft x 175 ft. C) 50 ft x 300 ft. D) 100ft x 200ft. Show Answer Correct Answer: D) 100ft x 200ft. 26. $Evaluate\\lim_{x\rightarrow3}\left[\frac{x^2-9}{x-3}\right]$ A) 2. B) 6. C) 1. D) 4. Show Answer Correct Answer: B) 6. 27. What is the derivative of sec(x)? A) Sec(x)tan(x). B) -csc(x)cot(x). C) -sec(x)tan(x). D) Csc(x)cot(x). Show Answer Correct Answer: A) Sec(x)tan(x). 28. $\lim_{x\rightarrow2}=\frac{x^4-16}{x-2}$ A) 32. B) 16. C) 4. D) None of the above. Show Answer Correct Answer: A) 32. 29. What is the derivative of cot(x)? A) -sec$^{2}$(x). B) -csc$^{2}$(x). C) Sec$^{2}$(x). D) Csc$^{2}$(x). Show Answer Correct Answer: B) -csc$^{2}$(x). 30. $Evaluate\\lim_{x\rightarrow1}\\frac{x^2+1}{x+100}$ A) 2. B) 1/101. C) 2/101. D) 101. Show Answer Correct Answer: C) 2/101. 31. $A'=\frac{-2\left(x-12\right)\left(x+12\right)}{x^2}$ A) Plug in 12 and-12, resulting in a maximum. B) Plug in 10 and 14, resulting in a minimum. C) Plug in 10 and 14, resulting in a maximum. D) Take the derivative of the expression. Show Answer Correct Answer: C) Plug in 10 and 14, resulting in a maximum. 32. If y=2x-8, what is the minimum value of the product xy? A) -16. B) -8. C) 2. D) -4. Show Answer Correct Answer: B) -8. 33. Use the derivative rules to find the derivative of the function f(x) = (3x-4)$^{2}$ A) F '(x) = 12x-16. B) F '(x) = 18x-24. C) F '(x) = 6x-8. D) F '(x) = 9. Show Answer Correct Answer: B) F '(x) = 18x-24. 34. Find the derivative $x^2\left(-3x^2-2\right)$ A) $12x^3+4x$. B) $-36x^2-4$. C) $-6x^3-4x$. D) $-12x^3-4x$. Show Answer Correct Answer: D) $-12x^3-4x$. 35. Find the derivative of the given equationf(x) = 1/x$^{2}$ A) 1/2x. B) -2x. C) -2x$^{-3}$. D) 2x. Show Answer Correct Answer: C) -2x$^{-3}$. 36. Evaluate $\lim_{x\rightarrow1}\left(x^2-2x+1\right)$ A) 0. B) 2. C) 3. D) 1. Show Answer Correct Answer: A) 0. 37. $\lim_{x\rightarrow3}=\frac{\sqrt[]{x+6}-x}{x-3}$ A) $\frac{6}{5}$. B) $\frac{5}{6}$. C) $\frac{-5}{6}$. D) $\frac{-6}{5}$. Show Answer Correct Answer: C) $\frac{-5}{6}$. 38. What is the derivative of a constant, C? A) C. B) 1. C) 0. D) None of the above. Show Answer Correct Answer: C) 0. 39. Find the derivative of the given equationf(x) = 7 A) 14. B) 7. C) 7x. D) 0. Show Answer Correct Answer: D) 0. 40. What is the Right-Hand Limit? A) Limit considering values of x less than c. B) Limit at x approaching infinity. C) Limit considering values of x greater than c. D) Limit at x = c. Show Answer Correct Answer: C) Limit considering values of x greater than c. 41. Nilai dari $\lim_{x\rightarrow0}\\frac{x^2-2x-1}{3x^2+6x-1}$ A) 1. B) 0. C) -3. D) 3. E) -1. Show Answer Correct Answer: A) 1. 42. What is the derivative of csc(x)? A) -csc(x)cot(x). B) -csc$^{2}$(x). C) -cot$^{2}$(x). D) Csc(x)cot(x). Show Answer Correct Answer: A) -csc(x)cot(x). 43. Use limits to find the area between the graph of y = 1/2x$^{3}$ and the x-axis from x = 0 to x = 4. A) 32/3. B) 64. C) 128. D) 32. Show Answer Correct Answer: D) 32. 44. Find f'(x) when f(x) = 3 A) 0. B) 1. C) 8. D) -6. Show Answer Correct Answer: A) 0. 45. $\lim_{x\rightarrow3}=\frac{2x^2-5x-3}{x-3}$ A) 1. B) 3. C) 7. D) None of the above. Show Answer Correct Answer: C) 7. 46. An object is thrown upward and its height at time $t$ $h(t) =-5t^2 + 20t + 2$ A) 25 meters. B) 18 meters. C) 22 meters. D) 12 meters. Show Answer Correct Answer: C) 22 meters. 47. Derivative means the same thing as A) Slope of the tangent line. B) Exponent. C) Slope of the normal line. D) Potato. Show Answer Correct Answer: A) Slope of the tangent line. 48. Find the derivative of $f(x) = 3x + 4$ A) $4$. B) $7$. C) $3x$. D) $3$. Show Answer Correct Answer: D) $3$. 49. Evaluate $\lim_{x\rightarrow0}\frac{x^2-9}{x^2-x-6}$ A) 0. B) $\frac{\text{3}}{\text{2}}$. C) Undefined. D) $\frac{\text{-3}}{\text{2}}$. Show Answer Correct Answer: B) $\frac{\text{3}}{\text{2}}$. 50. Let $f(x) = x^3-3x^2 + 2x$ $x = 0$ $x = 1$ $x = 3$ A) Increasing at $x=0$ $x=1$ $x=3$. B) Decreasing at $x=0$ $x=1$ $x=3$. C) Constant at all three points. D) Increasing at $x=0$ $x=1$ $x=3$. Show Answer Correct Answer: A) Increasing at $x=0$ $x=1$ $x=3$. 51. $\frac{\text{d}}{\text{d}x}\left(2x^{\pi}\right)$ A) $2\pi x^{\pi}-1$. B) $2\pi x^{-1}$. C) 2. D) 0. E) $2\pi x^{\left(\pi-1\right)}$. Show Answer Correct Answer: E) $2\pi x^{\left(\pi-1\right)}$. 52. Evaluate $\lim_{x \to 0} \frac{x}{x}$ A) 1. B) 0. C) Does not exist. D) Infinity. Show Answer Correct Answer: A) 1. 53. Find the derivative of f(x) = 6x$^{30 }$-2x$^{15}$ + 4x$^{3}$-2x + 1 A) F'(x) = 18x$^{29 }$+ 30x$^{15}$ + 12x$^{3 }$. B) F'(x) = 180x$^{29}$-30x$^{14 }$+ 12x$^{2}$-2. C) F'(x) = 180x$^{29}$-30x$^{14 }$+ 12x$^{2}$. D) F'(x) = 180x$^{29}$-30x$^{14 }$+ 12x$^{2}$ +1. Show Answer Correct Answer: B) F'(x) = 180x$^{29}$-30x$^{14 }$+ 12x$^{2}$-2. 54. If f(x) = x$^{100}$ + x$^{99}$ + ..... + x + 1, then f'(1) is equal to A) 5049. B) 5051. C) 50051. D) 5050. Show Answer Correct Answer: D) 5050. 55. Find f'(x) when $f\left(x\right)=4x^2-3+\frac{3}{x^2}$ A) $4x+3+\frac{3}{x^3}$. B) $2x+1$. C) $8x^2+7-\frac{6}{x^2}$. D) $8x-\frac{6}{x^3}$. Show Answer Correct Answer: D) $8x-\frac{6}{x^3}$. 56. If $f(x) = x^3 + 2x + 5$ $f'(x)$ A) $3x^2 + 2$. B) $3x^2 + 2x$. C) $3x^2 + 2x + 5$. D) $x^2 + 2$. Show Answer Correct Answer: A) $3x^2 + 2$. 57. If the derivative of a function at a point is negative, what does this tell you about the function at that point? A) The function is constant. B) The function is increasing. C) The function has a maximum. D) The function is decreasing. Show Answer Correct Answer: D) The function is decreasing. 58. Find the derivative of y = 2x$^{2}$ (3x-4) A) 6x-4. B) 15x$^{2 }$-6x. C) 6x$^{3}$-8x$^{2}$. D) 18x$^{2}$-16x. Show Answer Correct Answer: D) 18x$^{2}$-16x. 59. Differentiate y= 12x$^{-2}$ A) 24x$^{-1}$. B) 6x$^{-3}$. C) -24x$^{-1}$. D) -24x$^{-3}$. Show Answer Correct Answer: D) -24x$^{-3}$. 60. Acceleration is the rate at which the velocity of a moving object changes. That is, acceleration is the derivative of velocity. If time is measured in seconds and velocity in feet per second, then acceleration is measured in feet per second squared. If a car's velocity is described by the function $v\left(t\right)=16+3t+\frac{1}{4}t^2$ A) 32 feet per second squared. B) 37 feet per second squared. C) 5 feet per second squared. D) 18 feet per second squared. Show Answer Correct Answer: C) 5 feet per second squared. ← PreviousNext →Related QuizzesScience QuizzesClass 11 QuizzesClass 11 Mathematics Chapter 13 Limits And Derivatives Quiz 1Class 11 Mathematics Chapter 13 Limits And Derivatives Quiz 3Class 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