Let u 1 , u 2 , u 3 , υ 1 , υ 2 , υ 3 , w 1 , w 2 , and w 3 , be differentiable functions of t . Use Exercise 54 to show that d d t u 1 u 2 u 3 υ 1 υ 2 υ 3 w 1 w 2 w 3 = u ′ 1 u ′ 2 u ′ 3 υ 1 υ 2 υ 3 w 1 w 2 w 3 + u 1 u 2 u 3 υ ′ 1 υ ′ 2 υ ′ 3 w 1 w 2 w 3 + u 1 u 2 u 3 υ 1 υ 2 υ 3 w ′ 1 w ′ 2 w ′ 3
Let u 1 , u 2 , u 3 , υ 1 , υ 2 , υ 3 , w 1 , w 2 , and w 3 , be differentiable functions of t . Use Exercise 54 to show that d d t u 1 u 2 u 3 υ 1 υ 2 υ 3 w 1 w 2 w 3 = u ′ 1 u ′ 2 u ′ 3 υ 1 υ 2 υ 3 w 1 w 2 w 3 + u 1 u 2 u 3 υ ′ 1 υ ′ 2 υ ′ 3 w 1 w 2 w 3 + u 1 u 2 u 3 υ 1 υ 2 υ 3 w ′ 1 w ′ 2 w ′ 3
Let
u
1
,
u
2
,
u
3
,
υ
1
,
υ
2
,
υ
3
,
w
1
,
w
2
,
and
w
3
,
be differentiable functions of t. Use Exercise 54 to show that
d
d
t
u
1
u
2
u
3
υ
1
υ
2
υ
3
w
1
w
2
w
3
=
u
′
1
u
′
2
u
′
3
υ
1
υ
2
υ
3
w
1
w
2
w
3
+
u
1
u
2
u
3
υ
′
1
υ
′
2
υ
′
3
w
1
w
2
w
3
+
u
1
u
2
u
3
υ
1
υ
2
υ
3
w
′
1
w
′
2
w
′
3
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
Let f be a function whose graph consists of 5 line segments and a semicircle as shown in the figure below.
Let g(x) = √ƒƒ(t) dt .
0
3
2
-2
2
4
5
6
7
8
9
10
11
12
13
14
15
1. g(0) =
2. g(2) =
3. g(4) =
4. g(6) =
5. g'(3) =
6. g'(13)=
The expression 3 | (3+1/+1)
of the following integrals?
A
Ов
E
+
+
+ +
18
3+1+1
3++1
3++1
(A) √2×14 dx
x+1
(C) 1½-½√ √ ² ( 14 ) d x
(B) √31dx
(D) So 3+x
-dx
is a Riemann sum approximation of which
5
(E) 1½√√3dx
2x+1
2. Suppose the population of Wakanda t years after 2000 is given by the equation
f(t) = 45000(1.006). If this trend continues, in what year will the population reach 50,000
people? Show all your work, round your answer to two decimal places, and include units. (4
points)
University Calculus: Early Transcendentals (4th Edition)
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