# MTH 241 Past Questions/Answers

FBQ1: A convergent sequence has only ________________ limit(s)
`Answer: One`
FBQ2: If a sequence {Xn} is convergent then it is________________
```Answer: Bounded

FBQ3: A sequence  {(-1)n} is__________________________```
FBQ5: The sequence converges to ________________
```Answer: Bounded

FBQ4: A sequence  is ________________
Answer: convergent

Answer: 0.5```
FBQ7: Every Cauchy sequence is ________________.
```FBQ6:  is ________________
Answer: 0.5

Answer: Bounded```
FBQ9: Let {Xn}be a convergent sequence. is ________________
```FBQ8: A sequence of real number {Xn} is Cauchy if and only if ________________
Answer: Convergent

Answer: X```
FBQ11: If a sequence is increasing, then it may converge to its ________________
```FBQ10: If a sequence is decreasing, then it may converge to its ________________
Answer: Infimum

Answer: Supremum

FBQ12: A product of two convergent sequences is________________```
Answer: Null
```Answer: Convergent

FBQ13: Let   is ________________(Ans to 3 decimal point)
Answer: 1.618

FBQ14: A sequence of real numbers that converges to zero is known as ________________sequence```
Answer: False
```FBQ15: If a sequence does not have a limit, it is also called an ________________sequence
Answer: Oscillating

FBQ16: Every set of real numbers has a minimum_____________ (True or False)

FBQ17: Every set of real numbers has a maximum_____________ (True or False)```

FBQ20: There exists a set of real numbers with a supremum but no maximum_____________ (True or False)
```Answer: False

FBQ18: Every set of real numbers which is bounded above has a maximum_____________ (True or False)
Answer: False

FBQ19: Every set of real numbers which is bounded below has a minimum_____________ (True or False)
Answer: False

Answer: True```
FBQ25: A number which is neither positive nor negative is
```FBQ21: The  is _______
Answer: 2

FBQ22: " + " is  ___________  operation on
Answer: binary operation

FBQ23:  If a real number is not rational then it is  an  _______
Answer: Integer

FBQ24: If a real number is not rational then it is an __________ number
Answer: Irrational```
FBQ29: is an example of ___________ numbers
```Answer: 0

FBQ26: The supremum  is also called the ____ upper bound
Answer: Least

FBQ27: The harmonic series  ____
Answer: Diverges

FBQ28: A monotone sequence of real numbers is properly divergent if and only if it is _______
Answer: Unbounded

Answer: Irrational```
FBQ34: Give the next 3 terms of the sequence 0,1,1,2,3,5,8,………,____
```FBQ30: Concept of the divisibility only exists in set of __________
Answer: Integers

FBQ31: The limit of  n+1n√n is
Answer: 0

FBQ32: A convergent sequence has only ______________ limit(s)
Answer: 1

FBQ33: Every convergent sequence has ___________one limit
Answer: 7

Answer: 13, 21, 34```
FBQ37: A sequence in which the consecutive terms have opposite signs is called________________ sequence
```FBQ35: Two   Sets A and B are said to be _______ if and only if they have the same elements but possibly with different listings.
Answer: Equal

FBQ36: A sequence which does not converge to some real number is said to be________________
Answer: Divergent

Answer: Alternating

FBQ38:
Answer: x<=y

FBQ39: If is an ________________
Answer: Interval```
FBQ44: The range of is________________
```FBQ40: A sequence {Xn} is convergent to the limit if and only if all of its…________________.converge to the same limit ___________
Answer: Terms

FBQ41: The range of is________________
Answer: (0,3]

FBQ42: A continuous real-valued function defined on a closed and bounded interval ________________ be bounded
Answer: Must

FBQ43: The range of is________________
Answer: (-1/2, 1/2)

Answer: [-1/2, ½]

FBQ45:
Answer: 1

FBQ46:
Answer: 0.5

FBQ47:
Answer: 0.5```
MCQ13:
```FBQ48: Given the set
Answer: 2

FBQ49: what is the value of a____________
Answer: 0

FBQ50:
Answer: Complete

MCQ1: Define a sequence  Then the values of are
Answer:

MCQ2:
Answer:

MCQ3:
Answer:

MCQ4: Define
Answer: 0

MCQ5:
Answer: r

MCQ6: Consider the function
Answer: 1

MCQ7: Consider the function.                                 Then
Answer: 0

MCQ8:
Answer: None of the options

MCQ9:
Answer: 2

MCQ10:
Answer:

MCQ11:
Answer: 2

MCQ12:
Answer: 1

Answer:```
MCQ24: Solve the inequality Express your answer in interval notation.
```MCQ14: The inequality
Answer:

MCQ15: Solve the equation
Answer:

MCQ16: Find all which satisfy
Answer:

MCQ17: Solve the inequality Express your answer in interval notation
Answer:

MCQ18: Solve the equation
Answer:

MCQ19:
Answer:

MCQ20:
Answer:

MCQ21:  Solve the inequality Express your answer in interval notation.
Answer:

MCQ22:   Find all which satisfy
Answer:

MCQ23:  Solve the inequality Express your answer in interval notation.
Answer:```
MCQ43:
```Answer:

MCQ25:  Solve the equation
Answer:

MCQ26:
Answer: 3/4

MCQ27: Let   The domain of is the set of all real numbers except
Answer:

MCQ28:
Answer:

MCQ29: Consider the function
Answer:

MCQ30: Consider the function is
Answer:

MCQ31:
Answer:

MCQ32:
Answer:

MCQ33:
Answer:

MCQ34:
Answer:

MCQ35:
Answer:

MCQ36: Let
Answer: 2-32

MCQ37:
Answer: -4

MCQ38:
Answer: 6

MCQ39:
Answer: -1

MCQ40:
Answer: 1

MCQ41: Let
Answer: 3

MCQ42: Let
Answer: 5```
Answer: n

```Answer: 13

MCQ44:
Answer: Does not exist

MCQ45:
Answer: 1

MCQ46:
Answer: 2

MCQ47:
Answer: Does not exist

MCQ48:
Answer: -2, 3

MCQ49: An example of a positive convergent sequence
Answer:```
MCQ50: An example of a positive divergent sequence

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