Question

Math help please!

Answer 1

\[\frac{b-a}{n}=\frac{3}{n}\]
just choose b and a such that this equation holds
where b>a

Answer 2

once you do that we will move on to the rest

Answer 3

b=5 and a=2

Answer 4

sounds good you could also have chosen b=3 and a=0
but that works too
(you can choose a whole of bunch of things obviously :p)

Answer 5

Oh I hadn't thought of those

Answer 6

\[\int\limits_2^5 f(x) dx \text{ is what we have so far } \\ \text{ so we need } f(a+i \cdot \Delta x)=1+i \cdot \frac{3}{n} \]
so now we need to choose a function f such that this true
let me rewrite just a little:
a is 2 you chose this
and Delta x = (5-2)/n or 3/n
so you have
\[f(2+i \frac{3}{n})=1+i \frac{3}{n}\]

Answer 7

so we need to choose a function f such that this is true

Answer 8

like say we have f(x)=x-1
what would this give you if you replace x with 2+i*3/n

Answer 9

x?

Answer 10

we want to choose f such that:
\[f(2+i \frac{3}{n})=1+i \frac{3}{n} \\ \text{ I suggested } f(x)=x-1 \\ \text{ since if we replace } x \text{ with } 2+i \frac{3}{n} \\ \text{ we do get } \\ f(2+i \frac{3}{n})=2+i \frac{3}{n}-1 \text{ which is equal to } 1+i \frac{3}{n}\]

Answer 11

which is what we wanted

Answer 12

\[\int\limits_2^5 (x-1) dx\]
is one possibility on how we could choose the integral

Answer 13

So then I integrate it?

Answer 14

it just says write the integral

Answer 15

Oh thats not one of the choices :(

Answer 16

well you choose the upper and lower limit to be 5 and 2 respectively

Answer 17

if there are choices then that is a hint on how to choose the limit to get the integral they want

Answer 18

so what are the limit choices in the multiple choice?

Answer 19

so you do know 4-1=3 right?
of course you do
so we could have chosen b to be 4 and a to be 1

Answer 20

see if you can find the proper function by using our example above when we chose our limits to be 2 and 5

Answer 21

Haha okay

Answer 22

Im thinking its B where the limits are 1 to 4 of x

Answer 23

so this means you think
\[f(1+i \frac{3}{n})=1+i \frac{3}{n} \text{ means } f(x)=x\]
?

Answer 24

don't be afraid to say yes :)

Answer 25

Yes I think so

Answer 26

that is true

Answer 27

and your answer is right
if you do replace the x's in f(x)=x with 1+i*3/n you do get
f(1+i3/n)=1+i3/n
great job

Answer 28

do you have any questions

Answer 29

No thank you so much!! You were very helpful!!