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Unit 2: Functions, limit and continuity - Practice Quiz

MTH110 — Remedial Mathematics 60 Questions
0 Correct 0 Wrong 60 Left
0/60

1 A relation from set to set is called a function if every element of has:

functions Easy
A. No image in
B. Exactly one image in
C. More than one image in
D. At least two images in

2 If , then the value of is:

functions Easy
A.
B.
C.
D.

3 The set of all possible input values of a function is called its:

functions Easy
A. Domain
B. Image
C. Codomain
D. Range

4 The function , where is a fixed real number, is called a:

some specific types of functions Easy
A. Signum function
B. Identity function
C. Constant function
D. Modulus function

5 The identity function is defined as:

some specific types of functions Easy
A.
B.
C.
D.

6 The value of the modulus function at is:

some specific types of functions Easy
A.
B.
C.
D.

7 If and , then equals:

algebra of real functions Easy
A.
B.
C.
D.

8 If and , then equals:

algebra of real functions Easy
A.
B.
C.
D.

9 For the quotient function to be defined, we require that:

algebra of real functions Easy
A.
B.
C.
D.

10 The value of is:

limits Easy
A.
B.
C.
D.

11 A limit exists only if:

limits Easy
A. Left-hand and right-hand limits are equal
B.
C. is defined
D. The function is a polynomial

12 If and , then equals:

algebra of limits Easy
A.
B.
C.
D.

13 If and , then equals:

algebra of limits Easy
A.
B.
C.
D.

14 The value of is:

limits of polynomials and rational functions Easy
A.
B.
C.
D.

15 The value of is:

limits of polynomials and rational functions Easy
A.
B.
C.
D.

16 The value of is:

limits of trigonometric functions Easy
A.
B.
C. Undefined
D.

17 The value of is:

limits of trigonometric functions Easy
A.
B.
C.
D.

18 A function is continuous at if:

continuity Easy
A.
B.
C.
D. does not exist

19 Which of the following functions is continuous everywhere on ?

continuity Easy
A.
B.
C.
D.

20 If and are both continuous at , then is:

algebra of continuous functions Easy
A. Zero at
B. Continuous at
C. Undefined at
D. Discontinuous at

21 If , what is the domain of ?

functions Medium
A.
B.
C.
D.

22 The range of the function for is:

functions Medium
A.
B.
C.
D.

23 For the greatest integer function , what is the value of ?

some specific types of functions Medium
A.
B.
C.
D.

24 If , what is the value of for ?

some specific types of functions Medium
A.
B.
C.
D.

25 If and , what is ?

algebra of real functions Medium
A.
B.
C.
D.

26 If and , what is the domain of ?

algebra of real functions Medium
A.
B.
C.
D.

27 Evaluate .

limits Medium
A.
B. Does not exist
C.
D.

28 For the function , what can be said about ?

limits Medium
A. It does not exist
B. It equals
C. It equals
D. It equals

29 If and , what is ?

algebra of limits Medium
A.
B.
C.
D.

30 If and , which statement about is correct?

algebra of limits Medium
A. The limit equals
B. The quotient rule does not apply since the denominator limit is
C. The limit equals
D. The limit always exists and is infinite

31 Evaluate .

limits of polynomials and rational functions Medium
A.
B.
C.
D.

32 Evaluate .

limits of polynomials and rational functions Medium
A.
B.
C.
D.

33 Evaluate .

limits of polynomials and rational functions Medium
A.
B.
C.
D.

34 Evaluate .

limits of trigonometric functions Medium
A.
B.
C.
D.

35 Evaluate .

limits of trigonometric functions Medium
A.
B.
C.
D.

36 Evaluate .

limits of trigonometric functions Medium
A.
B.
C.
D.

37 For what value of is continuous at ?

continuity Medium
A.
B.
C.
D.

38 At which point is the function discontinuous?

continuity Medium
A. and
B. only
C. and
D. only

39 If and are both continuous everywhere, which conclusion is guaranteed by the algebra of continuous functions?

algebra of continuous functions Medium
A. is continuous everywhere
B. is continuous everywhere
C. is continuous only at
D. is continuous only where

40 The function is continuous on which set?

algebra of continuous functions Medium
A.
B.
C.
D.

41 Evaluate

limits of trigonometric functions Hard
A.
B.
C.
D.

42 Evaluate

limits of trigonometric functions Hard
A.
B.
C.
D.

43 Evaluate

limits of rational functions Hard
A.
B.
C.
D.

44 Evaluate

limits Hard
A.
B.
C.
D.

45 For what value of is continuous at ?

continuity Hard
A.
B.
C.
D.

46 Evaluate

limits Hard
A.
B.
C.
D.

47 Evaluate

limits of trigonometric functions Hard
A.
B.
C.
D.

48 If and , what is ?

algebra of limits Hard
A.
B.
C.
D.

49 Evaluate

limits of rational functions Hard
A.
B.
C.
D.

50 The function is:

continuity Hard
A. discontinuous at and
B. continuous everywhere but not differentiable at and
C. discontinuous only at
D. continuous and differentiable everywhere

51 Evaluate

limits of trigonometric functions Hard
A.
B.
C.
D.

52 The range of the function for is:

some specific types of functions Hard
A.
B.
C.
D.

53 Evaluate (Given .)

limits Hard
A.
B.
C.
D.

54 Let and . The domain of is:

algebra of real functions Hard
A.
B.
C.
D.

55 Evaluate

limits of rational functions Hard
A.
B.
C.
D.

56 Let with . For continuity at , must equal:

continuity Hard
A.
B.
C.
D.

57 Evaluate

limits of trigonometric functions Hard
A.
B.
C.
D.

58 Evaluate

limits Hard
A.
B.
C.
D.

59 If and are continuous at with , which statement is guaranteed true?

algebra of continuous functions Hard
A. is continuous at
B. is discontinuous at
C. is continuous only if
D. is continuous at

60 Evaluate where are positive integers.

limits of rational functions Hard
A.
B.
C.
D.
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