Determine a region whose area is equal to the given limit. do not evaluate the limit.

lim
n
→
[infinity]

n
∑
i
=
1

π
3
n
tan
(
i
π
3
n
)

a).
x
tan
x
on
[
0
,
π
3
]

b).
tan
x
on
[
0
,
3
π
]

c).
tan
x
on
[
−
π
3
,
π
3
]

d).
x
tan
x
on
[
−
π
3
,
π
3
]

e).
tan
x
on
[
0
,
π
3
]

step-by-step explanation:

its 512 because parenthesis and to the 2nd power is 512 so it will be 512

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.