APPLIED CALCULUS (WILEY PLUS)
6th Edition
ISBN: 9781119399322
Author: Hughes-Hallett
Publisher: WILEY
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Chapter 9.4, Problem 10P
To determine
To find:
The
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Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties
to find lim→-4
1
[2h (x) — h(x) + 7 f(x)] :
-
h(x)+7f(x)
3
O DNE
17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t).
(a) How much of the slope field can
you sketch from this information?
[Hint: Note that the differential
equation depends only on t.]
(b) What can you say about the solu-
tion with y(0) = 2? (For example,
can you sketch the graph of this so-
lution?)
y(0) = 1
y
AN
(b) Find the (instantaneous) rate of change of y at x = 5.
In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of
change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the
following limit.
lim
h→0
-
f(x + h) − f(x)
h
The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule
defining f.
f(x + h) = (x + h)² - 5(x+ h)
=
2xh+h2_
x² + 2xh + h² 5✔
-
5
)x - 5h
Step 4
-
The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x).
-
f(x + h) f(x) =
= (x²
x² + 2xh + h² -
])-
=
2x
+ h² - 5h
])x-5h) - (x² - 5x)
=
]) (2x + h - 5)
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Chapter 9 Solutions
APPLIED CALCULUS (WILEY PLUS)
Ch. 9.1 - Prob. 1PCh. 9.1 - Prob. 2PCh. 9.1 - Prob. 3PCh. 9.1 - Prob. 4PCh. 9.1 - Prob. 5PCh. 9.1 - Prob. 6PCh. 9.1 - Prob. 7PCh. 9.1 - Prob. 8PCh. 9.1 - Prob. 9PCh. 9.1 - Prob. 10P
Ch. 9.1 - Prob. 11PCh. 9.1 - Prob. 12PCh. 9.1 - Prob. 13PCh. 9.1 - Prob. 14PCh. 9.1 - Prob. 15PCh. 9.1 - Prob. 16PCh. 9.2 - Prob. 1PCh. 9.2 - Prob. 2PCh. 9.2 - Prob. 3PCh. 9.2 - Prob. 4PCh. 9.2 - Prob. 5PCh. 9.2 - Prob. 6PCh. 9.2 - Prob. 7PCh. 9.2 - Prob. 8PCh. 9.2 - Prob. 9PCh. 9.2 - Prob. 10PCh. 9.2 - Prob. 11PCh. 9.2 - Prob. 12PCh. 9.2 - Prob. 13PCh. 9.2 - Prob. 14PCh. 9.2 - Prob. 15PCh. 9.2 - Prob. 16PCh. 9.2 - Prob. 17PCh. 9.2 - Prob. 18PCh. 9.2 - Prob. 19PCh. 9.2 - Prob. 20PCh. 9.2 - Prob. 21PCh. 9.2 - Prob. 22PCh. 9.3 - Prob. 1PCh. 9.3 - Prob. 2PCh. 9.3 - Prob. 3PCh. 9.3 - Prob. 4PCh. 9.3 - Prob. 5PCh. 9.3 - Prob. 6PCh. 9.3 - Prob. 7PCh. 9.3 - Prob. 8PCh. 9.3 - Prob. 9PCh. 9.3 - Prob. 10PCh. 9.3 - Prob. 11PCh. 9.3 - Prob. 12PCh. 9.3 - Prob. 13PCh. 9.3 - Prob. 14PCh. 9.3 - Prob. 15PCh. 9.3 - Prob. 16PCh. 9.3 - Prob. 17PCh. 9.4 - Prob. 1PCh. 9.4 - Prob. 2PCh. 9.4 - Prob. 3PCh. 9.4 - Prob. 4PCh. 9.4 - Prob. 5PCh. 9.4 - Prob. 6PCh. 9.4 - Prob. 7PCh. 9.4 - Prob. 8PCh. 9.4 - Prob. 9PCh. 9.4 - Prob. 10PCh. 9.4 - Prob. 11PCh. 9.4 - Prob. 12PCh. 9.4 - Prob. 13PCh. 9.4 - Prob. 14PCh. 9.4 - Prob. 15PCh. 9.4 - Prob. 16PCh. 9.4 - Prob. 17PCh. 9.5 - Prob. 1PCh. 9.5 - Prob. 2PCh. 9.5 - Prob. 3PCh. 9.5 - Prob. 4PCh. 9.5 - Prob. 5PCh. 9.5 - Prob. 6PCh. 9.5 - Prob. 7PCh. 9.5 - Prob. 8PCh. 9.5 - Prob. 9PCh. 9.5 - Prob. 10PCh. 9.5 - Prob. 11PCh. 9.5 - Prob. 12PCh. 9.5 - Prob. 13PCh. 9.5 - Prob. 14PCh. 9.5 - Prob. 15PCh. 9.5 - Prob. 16PCh. 9.5 - Prob. 17PCh. 9.5 - Prob. 18PCh. 9.5 - Prob. 19PCh. 9.5 - Prob. 20PCh. 9.5 - Prob. 21PCh. 9.5 - Prob. 22PCh. 9.5 - Prob. 23PCh. 9.5 - Prob. 24PCh. 9.5 - Prob. 25PCh. 9.6 - Prob. 1PCh. 9.6 - Prob. 2PCh. 9.6 - Prob. 3PCh. 9.6 - Prob. 4PCh. 9.6 - Prob. 5PCh. 9.6 - Prob. 6PCh. 9.6 - Prob. 7PCh. 9.6 - Prob. 8PCh. 9.6 - Prob. 9PCh. 9.6 - Prob. 10PCh. 9.6 - Prob. 11PCh. 9.6 - Prob. 12PCh. 9.6 - Prob. 13PCh. 9.6 - Prob. 14PCh. 9.6 - Prob. 15PCh. 9.6 - Prob. 16PCh. 9.6 - Prob. 17PCh. 9.6 - Prob. 18PCh. 9.6 - Prob. 19PCh. 9.6 - Prob. 20PCh. 9.6 - Prob. 21PCh. 9.6 - Prob. 22PCh. 9.6 - Prob. 23PCh. 9.6 - Prob. 24PCh. 9.6 - Prob. 25PCh. 9.6 - Prob. 26PCh. 9.7 - Prob. 1PCh. 9.7 - Prob. 2PCh. 9.7 - Prob. 3PCh. 9.7 - Prob. 4PCh. 9.7 - Prob. 5PCh. 9.7 - Prob. 6PCh. 9.7 - Prob. 7PCh. 9.7 - Prob. 8PCh. 9.7 - Prob. 9PCh. 9.7 - Prob. 10PCh. 9.7 - Prob. 11PCh. 9.7 - Prob. 12PCh. 9 - Prob. 1SYUCh. 9 - Prob. 2SYUCh. 9 - Prob. 3SYUCh. 9 - Prob. 4SYUCh. 9 - Prob. 5SYUCh. 9 - Prob. 6SYUCh. 9 - Prob. 7SYUCh. 9 - Prob. 8SYUCh. 9 - Prob. 9SYUCh. 9 - Prob. 10SYUCh. 9 - Prob. 11SYUCh. 9 - Prob. 12SYUCh. 9 - Prob. 13SYUCh. 9 - Prob. 14SYUCh. 9 - Prob. 15SYUCh. 9 - Prob. 16SYUCh. 9 - Prob. 17SYUCh. 9 - Prob. 18SYUCh. 9 - Prob. 19SYUCh. 9 - Prob. 20SYUCh. 9 - Prob. 21SYUCh. 9 - Prob. 22SYUCh. 9 - Prob. 23SYUCh. 9 - Prob. 24SYUCh. 9 - Prob. 25SYUCh. 9 - Prob. 26SYUCh. 9 - Prob. 27SYUCh. 9 - Prob. 28SYUCh. 9 - Prob. 29SYUCh. 9 - Prob. 30SYUCh. 9 - Prob. 31SYUCh. 9 - Prob. 32SYUCh. 9 - Prob. 33SYUCh. 9 - Prob. 34SYUCh. 9 - Prob. 35SYUCh. 9 - Prob. 36SYUCh. 9 - Prob. 37SYUCh. 9 - Prob. 38SYUCh. 9 - Prob. 39SYUCh. 9 - Prob. 40SYUCh. 9 - Prob. 41SYUCh. 9 - Prob. 42SYUCh. 9 - Prob. 43SYUCh. 9 - Prob. 44SYUCh. 9 - Prob. 45SYUCh. 9 - Prob. 46SYUCh. 9 - Prob. 47SYUCh. 9 - Prob. 48SYUCh. 9 - Prob. 49SYUCh. 9 - Prob. 50SYUCh. 9 - Prob. 51SYUCh. 9 - Prob. 52SYUCh. 9 - Prob. 53SYUCh. 9 - Prob. 54SYUCh. 9 - Prob. 55SYUCh. 9 - Prob. 56SYUCh. 9 - Prob. 57SYUCh. 9 - Prob. 58SYUCh. 9 - Prob. 59SYUCh. 9 - Prob. 60SYUCh. 9 - Prob. 61SYUCh. 9 - Prob. 62SYUCh. 9 - Prob. 63SYUCh. 9 - Prob. 64SYUCh. 9 - Prob. 65SYUCh. 9 - Prob. 66SYUCh. 9 - Prob. 67SYUCh. 9 - Prob. 68SYUCh. 9 - Prob. 69SYUCh. 9 - Prob. 70SYUCh. 9 - Prob. 1FOTCh. 9 - Prob. 2FOTCh. 9 - Prob. 3FOTCh. 9 - Prob. 4FOTCh. 9 - Prob. 5FOTCh. 9 - Prob. 6FOTCh. 9 - Prob. 7FOTCh. 9 - Prob. 8FOTCh. 9 - Prob. 9FOTCh. 9 - Prob. 10FOTCh. 9 - Prob. 11FOTCh. 9 - Prob. 12FOTCh. 9 - Prob. 13FOTCh. 9 - Prob. 14FOTCh. 9 - Prob. 15FOTCh. 9 - Prob. 16FOTCh. 9 - Prob. 17FOTCh. 9 - Prob. 18FOTCh. 9 - Prob. 19FOTCh. 9 - Prob. 20FOTCh. 9 - Prob. 21FOT
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