# 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

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:

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