Limits and Continuity MCQ Test: Limits and Continuity MCQs - Practice Questions
1. What is the limit of the function f(x) = tan(x) as x approaches pi/2?
2. What is the limit of the function f(x) = (x^3 - 2x^2 + 4)/(x^2 - 4x + 4) as x approaches 2?
3. In calculus, what does the term 'continuity' refer to?
4. For which value of x is the function f(x) = sin(x)/x continuous?
5. Which theorem is used to evaluate limits involving trigonometric functions?
6. Which rule is applied to evaluate the limit of a function involving radicals?
7. What is the limit of a polynomial function as x approaches infinity?
8. Which type of limit involves the behavior of a function as x approaches a specific point?
9. For which value of x is the function f(x) = (x^2 - 1)/(x - 1) not defined?
10. What is the limit of the function f(x) = sin(1/x) as x approaches 0?
11. In calculus, what is the condition for a function to be continuous at a specific point?
12. What is the limit of the function f(x) = e^(1/x) as x approaches 0?
13. Which theorem states that if a function is continuous on a closed interval, then it attains its maximum and minimum values?
14. Which concept is used to define the instantaneous rate of change of a function at a point?
15. What is the limit of the function f(x) = cos(1/x) as x approaches 0?
16. For which value of x is the function f(x) = tan(x) not defined?
17. What is the definition of a limit in calculus?
18. What is the limit of the function f(x) = 1/(x - 2) as x approaches 2?
19. What is the limit of the function f(x) = sqrt(x) as x approaches 0 from the right?
20. What is the limit of the function f(x) = (e^x - x - 1)/(x^2) as x approaches infinity?
21. What is the limit of the function f(x) = (e^x - 1)/x as x approaches 0?
22. What is the limit of the function f(x) = ln(1 + e^x) as x approaches infinity?
23. What is the limit of the function f(x) = (1 - e^(-x))/x as x approaches infinity?
24. For which value of x is the function f(x) = 1/x continuous?
25. What is the limit of the function f(x) = (sin(x))/x as x approaches 0?
26. In calculus, what does the term 'discontinuity' refer to?
27. In calculus, what does the term 'asymptote' refer to?
28. What is the limit of the function f(x) = 1/x as x approaches negative infinity?
29. In calculus, what does the term 'indeterminate form' refer to?
30. What is the limit of the function f(x) = (tan^2(x))/(x^2) as x approaches 0?
31. For which value of x is the function f(x) = 1/x not defined?
32. Which theorem is used to find limits involving indeterminate forms like 0/0 or infinity/infinity?
33. What is the limit of the function f(x) = (1 - cos(x))/x^2 as x approaches 0?
34. Which property allows you to factor out constants when finding limits?
35. What is the limit of the function f(x) = arctan(1/x) as x approaches 0?
36. What is the limit of the function f(x) = ln(1 + x) as x approaches 0?
37. What is the limit of a constant function as x approaches any value?
38. Which theorem guarantees the existence of the limit of a function on a closed interval?
39. What is the limit of the function f(x) = 1/(x^2) as x approaches 0?
40. What is the limit of the function f(x) = x^2 - 4x + 4 as x approaches 2?
41. What is the limit of the function f(x) = 1/x as x approaches 1?
42. What is the limit of the function f(x) = ln(x) as x approaches 0 from the right?
43. What is the limit of the function f(x) = 1/x as x approaches 0 from the left?
44. Which rule is used to find limits of rational functions?
45. In calculus, what is the definition of a removable discontinuity?
46. What is the limit of the function f(x) = 1/x as x approaches infinity?
47. Which type of limit involves the behavior of a function as x approaches positive or negative infinity?
48. Which rule is applied to evaluate the limit of a function containing exponentials?
49. What is the limit of the function f(x) = e^(1/x) as x approaches 0 from the left?
50. What is the limit of the function f(x) = 1/sin(x) as x approaches 0?