Environment of Forests Following the lead of the National Wildlife Federation, the Department of the Interior of a South American country began to record an index of environmental quality that measured progress and decline in the environmental quality of its forests. The index for the years 2004 through 2014 is approximated by the function I ( t ) = 1 3 t 3 − 5 2 t 2 + 80 (0 ≤ t ≤ 10) where t = 0 corresponds to 2004. Find the intervals where the function I is increasing and the intervals where it is decreasing. Interpret your results.
Environment of Forests Following the lead of the National Wildlife Federation, the Department of the Interior of a South American country began to record an index of environmental quality that measured progress and decline in the environmental quality of its forests. The index for the years 2004 through 2014 is approximated by the function I ( t ) = 1 3 t 3 − 5 2 t 2 + 80 (0 ≤ t ≤ 10) where t = 0 corresponds to 2004. Find the intervals where the function I is increasing and the intervals where it is decreasing. Interpret your results.
Solution Summary: The author explains the formula to calculate the differential of a function h(x)=13t3. It interprets that from 2000 to 2005 the environment quality of forests decline
Environment of Forests Following the lead of the National Wildlife Federation, the Department of the Interior of a South American country began to record an index of environmental quality that measured progress and decline in the environmental quality of its forests. The index for the years 2004 through 2014 is approximated by the function
I
(
t
)
=
1
3
t
3
−
5
2
t
2
+
80
(0 ≤ t ≤ 10)
where t = 0 corresponds to 2004. Find the intervals where the function I is increasing and the intervals where it is decreasing. Interpret your results.
EXAMPLE 3
Find
S
X
√√2-2x2
dx.
SOLUTION Let u = 2 - 2x². Then du =
Χ
dx =
2- 2x²
=
信
du
dx, so x dx =
du and
u-1/2 du
(2√u) + C
+ C (in terms of x).
Let g(z) =
z-i
z+i'
(a) Evaluate g(i) and g(1).
(b) Evaluate the limits
lim g(z), and lim g(z).
2-12
(c) Find the image of the real axis under g.
(d) Find the image of the upper half plane {z: Iz > 0} under the function g.
Chapter 4 Solutions
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
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