MTH 241 Past Questions/Answers

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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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