Let {an} be a bounded sequence of numbers in r. we define a new sequence bn} as follows sup{an n n} = 1. prove that {by} is monotone. definition. if {an} is a bounded sequence in r, then the limsup, denoted lim sup an, is defined as: n oo lim sup an n > n} lim sup an (1) noo n oo 2. prove that the limit in (1) exists. 3. based on the definition of the lim sup above, what would the definition of lim inf be? 4. using the definition you gave in the previous problem, show that for bounded sequences, the lim inf always exists 5. prove that if lm sup{an} lim inffan} l. then the limit of {an} exists and equals l

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?

1. 3. can also be expressed as (22/7)

2. -4.5

3. 3.6

happy to

pls mark as brainliest

(0.2)+(-8)=0.3+-3+0.3m is the equation i guess? ?

step-by-step explanation: