MT1940 (Analysis) Definitions

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  • Created by: wxrpaint
  • Created on: 08-01-16 16:00
U W U M U U S L B T B L P A R M V I G R J
E P W L N P C K L R E J X V Q G W Y B O M
G X S E G H T U R Y F X X E R H H V U A K
E S L K V J M V C O J R L J F M O M O D I
E V X B W D X Q T B N B O I W K G J V T G
T X S U B N B O U N D E D A B O V E C X W
X V K R I B K T X G H J S L I P U A W H E
V Y V K M E K C B P A B S U K S A Q N X J
B O U N D E D S E Q U E N C E A S U B N X
N V P R O P E R L Y D I V E R G E N T H Y
C D J J T S U Y F R O T H O L H D J Y H A
T R M O N O T O N I C S E Q U E N C E I M
M V G A B S O L U T E M A X I M U M M G G
S T B O U N D E D F U N C T I O N F A R Q
S U B S E Q U E N C E O F X S U B N Q R T
T I N T E R S E C T I O N O F X A N D Y J
U O I L G S O L X S K S V M W R M D S I X
F B A S U B N C O N V E R G E S T O A P G
U Q I C O N T I N U I T Y E D D E F Q W G
G E K R L T C W K O K P I F G M P B C G A
F L P P F W E X M M K D O S C P A D C J J

Clues

  • every z that is an element of X and an element of Y (12, 2, 1, 3, 1)
  • for all E greater than 0, there exists d greater than 0 such that for all x in A with |x-c| less than d, we have |f(x)-f(c)| less than E (10, 1, 1, 3)
  • for all E greater than 0, there is some N in N such that, for all n greater than N, we have |a sub n - a| less than E (1, 3, 1, 9, 2, 1)
  • for n1 less than n2 less than n3... strictly increasing seq. of natural numbers, (x sub n sub i) is subseq. (11, 2, 1, 3, 1)
  • it is increasing or decreasing (9, 8)
  • lim(n to infinity)(x sub n) = (-)infinity (8, 9)
  • some t in A such that f(t) greater than/equal to f(x) for all x in A (8, 7)
  • some u in R such that x sub n less than/equal to u for all n in N (1, 3, 1, 7, 5)
  • there exists M greater than 0 such that, for all x in A, |f(x)| less than/equal to M (7, 8, 1, 1, 1)
  • there is some M in R with M greater than zero such that |a sub n| less than/equal to M for all n in N (7, 8, 1, 3, 1)

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