# (b) Determine the general formula for f bar(subscript [0, x] the average of cos t over the interval [0, x]. please answer # b. The entire question is: (a) Find the average value of cos t on...

- (b) Determine the general formula for f bar(subscript [0, x] the average of cos t over the interval [0, x].

please answer # b. The entire question is:

(a) Find the average value of cos t on the intervals [0, π],[0,(π/2)],[ 0,(π/4)],[0, 0.01].

(b) Determine the general formula for f bar (the letter f with a bar over it) (subscript [0, x] the average of cos t over the interval [0, x].

(c) Calculate lim(x->0) f bar (the letter f with a bar over it) (subscript [0, x])

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### 1 Answer

To determine the general formula for the average of `cos t` over the interval `[0,x]` , we use the formula `1/{b-a}int_a^b f(t)dt`.

This means that the average is

`1/x int_0^x cos t dt`

`=1/x (sin t|_0^x`

`=1/x (sin x - sin 0)`

`=sin x / x`

**The general formula for f bar is `sin x /x` **