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Unit 4: Calculus - Practice Quiz

CSE333 — Combinatorial Studies-I 60 Questions
0 Correct 0 Wrong 60 Left
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1 Evaluate .

limits Easy
A.
B.
C.
D.

2 Evaluate .

limits Easy
A.
B.
C.
D.

3 Evaluate .

limits Easy
A.
B.
C.
D.

4 If the left-hand and right-hand limits of a function at are equal, what can be concluded?

limits Easy
A. The function is increasing
B. The limit exists
C. The function is constant
D. The derivative is zero

5 Which condition is required for a function to be continuous at ?

continuity Easy
A.
B.
C.
D.

6 Which function is continuous for every real number?

continuity Easy
A.
B.
C.
D.

7 At which point is discontinuous?

continuity Easy
A.
B.
C.
D.

8 What is the derivative of ?

differentiability Easy
A.
B.
C.
D.

9 What is the derivative of the constant function ?

differentiability Easy
A.
B.
C.
D.

10 If a function is differentiable at , which statement must be true?

differentiability Easy
A. It has a maximum at
B. It is constant near
C. It has a minimum at
D. It is continuous at

11 For , where does the function attain its minimum value?

maxima and minima Easy
A.
B.
C.
D.

12 If , what is commonly called?

maxima and minima Easy
A. A critical point
B. An inflection interval
C. A limit point
D. A boundary value

13 For , what is the maximum value of the function?

maxima and minima Easy
A.
B.
C.
D.

14 Which conditions are required by the Mean Value Theorem on ?

mean value theorem Easy
A. Differentiable on and constant on
B. Continuous on and differentiable on
C. Continuous on and bounded on
D. Increasing on and differentiable on

15 According to the Mean Value Theorem, there exists some such that equals which expression?

mean value theorem Easy
A.
B.
C.
D.

16 For on , what value of satisfies the Mean Value Theorem?

mean value theorem Easy
A.
B.
C.
D.

17 Evaluate the indefinite integral .

integration Easy
A.
B.
C.
D.

18 What does the constant represent in an indefinite integral?

integration Easy
A. The upper integration limit
B. The variable of integration
C. The lower integration limit
D. The constant of integration

19 Evaluate .

integration Easy
A.
B.
C.
D.

20 Evaluate the definite integral .

integration Easy
A.
B.
C.
D.

21 Evaluate .

limits Medium
A.
B.
C.
D.

22 Evaluate .

limits Medium
A. The limit does not exist because both the numerator and denominator approach infinity.
B.
C.
D.

23 If , what is the value of ?

limits Medium
A.
B.
C.
D.

24 Let For which value of is continuous at ?

continuity Medium
A.
B.
C.
D.

25 On which interval is continuous?

continuity Medium
A. The function is continuous over all real numbers because its numerator is a polynomial.
B.
C.
D.

26 The function for is extended continuously to . What must equal?

continuity Medium
A.
B.
C.
D.

27 Let If is differentiable at , which pair is required?

differentiability Medium
A.
B.
C.
D.

28 The curve defines implicitly as a differentiable function of near . What is at ?

differentiability Medium
A.
B.
C.
D.

29 If , what is at ?

differentiability Medium
A.
B.
C.
D.

30 For , which statement correctly classifies its stationary points?

maxima and minima Medium
A. Local maxima occur at both and .
B. Local minima occur at both and .
C. A local maximum occurs at and a local minimum occurs at .
D. A local minimum occurs at and a local maximum occurs at .

31 A rectangle has perimeter units. What is the maximum possible area of the rectangle?

maxima and minima Medium
A. square units
B. square units
C. The area increases without bound as one side becomes much longer than the other side.
D. square units

32 What are the absolute minimum and maximum values, respectively, of on ?

maxima and minima Medium
A. Minimum , maximum
B. Minimum , maximum
C. Minimum , maximum
D. Minimum , maximum

33 For on , which value of satisfies the conclusion of the Mean Value Theorem?

mean value theorem Medium
A.
B.
C.
D.

34 For on , which value of is guaranteed by Rolle's theorem?

mean value theorem Medium
A. Every point in satisfies Rolle's theorem because both endpoint values are zero.
B.
C.
D.

35 Suppose is differentiable on , , and throughout the interval. Which interval must contain ?

mean value theorem Medium
A.
B.
C.
D.

36 Evaluate .

integration Medium
A.
B.
C.
D.

37 Evaluate .

integration Medium
A.
B.
C.
D.

38 Find the area enclosed by the curves and between their intersection points.

integration Medium
A.
B.
C.
D.

39 Evaluate .

integration Medium
A.
B.
C.
D.

40 Let . What is ?

integration Medium
A.
B.
C.
D.

41 Evaluate

limits Hard
A.
B.
C.
D.

42 Evaluate

limits Hard
A.
B.
C.
D.

43 Evaluate

limits Hard
A.
B.
C.
D.

44 Define For which relation between and is continuous at ?

continuity Hard
A.
B.
C.
D.

45 Let What is the complete set of points at which is continuous?

continuity Hard
A.
B.
C.
D.

46 For real parameters and , define Which condition is necessary and sufficient for continuity at ?

continuity Hard
A. for every
B. if , and if
C. for every
D. if , and if

47 Let Which statement correctly describes the behavior of at ?

differentiability Hard
A. is differentiable, but is discontinuous at
B. has a continuous first derivative, but does not exist
C. is continuous but not differentiable at
D. is twice differentiable, but is discontinuous at

48 Define What is ?

differentiability Hard
A.
B.
C.
D.

49 Let and let . Since , determine .

differentiability Hard
A.
B.
C.
D.

50 What are the global minimum and global maximum, respectively, of on

maxima and minima Hard
A. and
B. and
C. and
D. and

51 For on , which pair gives its global minimum and global maximum, respectively?

maxima and minima Hard
A. and
B. and
C. and
D. and

52 For the family , for which values of does have exactly three distinct local extrema?

maxima and minima Hard
A.
B.
C.
D.

53 Rolle's theorem is applied to on . Which set contains all values of satisfying the theorem's conclusion?

mean value theorem Hard
A.
B.
C.
D.

54 Apply Cauchy's mean value theorem to and on , where . What value of is obtained?

mean value theorem Hard
A.
B.
C.
D.

55 For on , one has . Why does this not imply the existence of with ?

mean value theorem Hard
A. is not differentiable at
B. is not continuous at
C. has unequal one-sided limits at
D. is not bounded on

56 For which real values of does the improper integral converge, and what is its value?

integration Hard
A. , with value
B. , with value
C. , with value
D. , with value

57 Evaluate

integration Hard
A.
B.
C.
D.

58 For positive constants and , evaluate

integration Hard
A.
B.
C.
D.

59 For , evaluate the parameter-dependent integral

integration Hard
A.
B.
C.
D.

60 Evaluate the improper integral

integration Hard
A.
B.
C.
D.
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