Question

6.(8pts) Find the Average value of ?(?) = 5? sin(?^{2})
on the interval [ 0, √? ]

Answer #1

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Find the average of the function ?(?) = sin(?) + cos(2?) over
the interval 0 ≤ ? ≤ 2?.

Compute the average value of the function f ( s ) = sin^5 s
cos^6 son the interval [ 0 , π ]

1. Find the critical numbers of f=sin(x)-cos(x) at interval
[0,?].
If there is more more than one enter them as a comma separated
list. ?=
The maximum value of f on the interval is y=
2. Find the critical numbers of the function f(x)=
x1/6-x-5/6 x=

? ᇱᇱ(?) = 5 sin ?, ? ᇱ(0) = −2 and ?(0) = 4. Find ?(?).
Find the area of the region bounded by ? = −? ଶ − 2? + 3 and the
?-axis

If f(x) = sin(x^6), find the value of (f^(42))*0.

Set up an integral
that gives an average value x³ sin x
interval [-2, 1].

1. Use the given conditions to find the exact value of the
expression.
sin(α) = -5/3, tan(α) > 0, sin(α - 5π/3)
2. Use the given conditions to find the exact value of the
expression.
cos α = 24/25, sin α < 0, cos(α + π/6)
3. Use the given conditions to find the exact value of the
expression.
cot x = √3, cos x < 0, tan(x + π/6)
4. If α and β are acute angles such that...

(A.) Find the average value of the function f over the
interval [5, 7].
f(x) = 9 − x
(B.) Find the average value of the function f
over the interval [0, 5].
f(x) = (8)/(x+1)

Consider the function on the interval (0, 2π).
f(x) =
sin(x)/
2 + (cos(x))2
(a) Find the open intervals on which the function is increasing
or decreasing. (Enter your answers using interval notation.)
increasing
decreasing
(b) Apply the First Derivative Test to identify the relative
extrema.
relative maximum
(x, y) =
relative minimum
(x, y) =

Find the exact value sin(2arctan( −a/b ) + arccos(a)), where a
> 0, b > 0, and a^2 + b^2 =1

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