Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
4th Edition
ISBN: 9780134686974
Author: Michael Sullivan, Michael Sullivan III
Publisher: PEARSON
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Chapter 12.1, Problem 37AYU
To determine
To find: The measures of the three angles. Round to the nearest tenth.
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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 12 Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Ch. 12.1 - Prob. 1AYUCh. 12.1 - Prob. 2AYUCh. 12.1 - Prob. 3AYUCh. 12.1 - Prob. 4AYUCh. 12.1 - Prob. 5AYUCh. 12.1 - Prob. 6AYUCh. 12.1 - Prob. 7AYUCh. 12.1 - Prob. 8AYUCh. 12.1 - Prob. 9AYUCh. 12.1 - Prob. 10AYU
Ch. 12.1 - Prob. 11AYUCh. 12.1 - Prob. 12AYUCh. 12.1 - Prob. 13AYUCh. 12.1 - Prob. 14AYUCh. 12.1 - Prob. 15AYUCh. 12.1 - Prob. 16AYUCh. 12.1 - Prob. 17AYUCh. 12.1 - Prob. 18AYUCh. 12.1 - Prob. 19AYUCh. 12.1 - Prob. 20AYUCh. 12.1 - Prob. 21AYUCh. 12.1 - Prob. 22AYUCh. 12.1 - Prob. 23AYUCh. 12.1 - Prob. 24AYUCh. 12.1 - Prob. 25AYUCh. 12.1 - Prob. 26AYUCh. 12.1 - Analyzing Survey Data In a consumer survey of 500...Ch. 12.1 - Prob. 28AYUCh. 12.1 - Prob. 29AYUCh. 12.1 - Prob. 30AYUCh. 12.1 - Prob. 31AYUCh. 12.1 - Prob. 32AYUCh. 12.1 - Prob. 33AYUCh. 12.1 - Prob. 34AYUCh. 12.1 - Prob. 36AYUCh. 12.1 - Prob. 37AYUCh. 12.1 - Prob. 38AYUCh. 12.1 - Prob. 39AYUCh. 12.2 - Prob. 1AYUCh. 12.2 - Prob. 2AYUCh. 12.2 - Prob. 3AYUCh. 12.2 - Prob. 4AYUCh. 12.2 - Prob. 5AYUCh. 12.2 - Prob. 6AYUCh. 12.2 - Prob. 7AYUCh. 12.2 - Prob. 8AYUCh. 12.2 - Prob. 9AYUCh. 12.2 - Prob. 10AYUCh. 12.2 - Prob. 11AYUCh. 12.2 - Prob. 12AYUCh. 12.2 - Prob. 13AYUCh. 12.2 - Prob. 14AYUCh. 12.2 - Prob. 15AYUCh. 12.2 - Prob. 16AYUCh. 12.2 - Prob. 17AYUCh. 12.2 - Prob. 18AYUCh. 12.2 - Prob. 19AYUCh. 12.2 - Prob. 20AYUCh. 12.2 - Prob. 21AYUCh. 12.2 - Prob. 22AYUCh. 12.2 - Prob. 23AYUCh. 12.2 - Prob. 24AYUCh. 12.2 - Prob. 25AYUCh. 12.2 - Prob. 26AYUCh. 12.2 - Prob. 27AYUCh. 12.2 - Prob. 28AYUCh. 12.2 - Prob. 29AYUCh. 12.2 - Prob. 30AYUCh. 12.2 - Prob. 31AYUCh. 12.2 - Prob. 32AYUCh. 12.2 - Prob. 33AYUCh. 12.2 - Prob. 34AYUCh. 12.2 - Prob. 35AYUCh. 12.2 - Prob. 36AYUCh. 12.2 - Prob. 37AYUCh. 12.2 - Prob. 38AYUCh. 12.2 - Prob. 39AYUCh. 12.2 - Prob. 40AYUCh. 12.2 - Prob. 41AYUCh. 12.2 - Establishing Committees In how many ways can a...Ch. 12.2 - Prob. 43AYUCh. 12.2 - Prob. 44AYUCh. 12.2 - Prob. 45AYUCh. 12.2 - Prob. 46AYUCh. 12.2 - Prob. 47AYUCh. 12.2 - Prob. 48AYUCh. 12.2 - Prob. 49AYUCh. 12.2 - Prob. 50AYUCh. 12.2 - Forming Words How many different 9-letter words...Ch. 12.2 - Prob. 52AYUCh. 12.2 - Prob. 53AYUCh. 12.2 - Prob. 54AYUCh. 12.2 - Prob. 55AYUCh. 12.2 - Prob. 56AYUCh. 12.2 - Prob. 57AYUCh. 12.2 - Prob. 58AYUCh. 12.2 - Prob. 59AYUCh. 12.2 - Prob. 60AYUCh. 12.2 - Prob. 61AYUCh. 12.2 - Prob. 62AYUCh. 12.2 - Prob. 63AYUCh. 12.2 - Prob. 64AYUCh. 12.2 - Prob. 65AYUCh. 12.2 - Prob. 66AYUCh. 12.2 - Prob. 67AYUCh. 12.2 - Prob. 68AYUCh. 12.2 - Prob. 69AYUCh. 12.2 - Prob. 70AYUCh. 12.3 - When the same probability is assigned to each...Ch. 12.3 - Prob. 2AYUCh. 12.3 - Prob. 3AYUCh. 12.3 - Prob. 4AYUCh. 12.3 - Prob. 5AYUCh. 12.3 - Prob. 6AYUCh. 12.3 - Prob. 7AYUCh. 12.3 - Prob. 8AYUCh. 12.3 - Prob. 9AYUCh. 12.3 - Prob. 10AYUCh. 12.3 - Prob. 11AYUCh. 12.3 - Prob. 12AYUCh. 12.3 - Prob. 13AYUCh. 12.3 - Prob. 14AYUCh. 12.3 - Prob. 15AYUCh. 12.3 - Prob. 16AYUCh. 12.3 - Prob. 17AYUCh. 12.3 - Prob. 18AYUCh. 12.3 - Prob. 19AYUCh. 12.3 - Prob. 20AYUCh. 12.3 - Prob. 21AYUCh. 12.3 - Prob. 22AYUCh. 12.3 - Prob. 23AYUCh. 12.3 - Prob. 24AYUCh. 12.3 - Prob. 25AYUCh. 12.3 - Prob. 26AYUCh. 12.3 - Prob. 27AYUCh. 12.3 - Prob. 28AYUCh. 12.3 - Prob. 29AYUCh. 12.3 - Prob. 30AYUCh. 12.3 - Prob. 31AYUCh. 12.3 - Prob. 32AYUCh. 12.3 - Prob. 33AYUCh. 12.3 - Prob. 34AYUCh. 12.3 - Prob. 35AYUCh. 12.3 - Prob. 36AYUCh. 12.3 - Prob. 37AYUCh. 12.3 - Prob. 38AYUCh. 12.3 - Prob. 39AYUCh. 12.3 - Prob. 40AYUCh. 12.3 - Prob. 41AYUCh. 12.3 - Prob. 42AYUCh. 12.3 - Prob. 43AYUCh. 12.3 - Prob. 45AYUCh. 12.3 - Prob. 46AYUCh. 12.3 - Prob. 47AYUCh. 12.3 - Prob. 48AYUCh. 12.3 - Prob. 49AYUCh. 12.3 - Prob. 50AYUCh. 12.3 - Prob. 51AYUCh. 12.3 - Prob. 52AYUCh. 12.3 - Prob. 53AYUCh. 12.3 - Prob. 54AYUCh. 12.3 - Prob. 55AYUCh. 12.3 - For Problems 57-60, a golf ball is selected at...Ch. 12.3 - Prob. 57AYUCh. 12.3 - Prob. 58AYUCh. 12.3 - Prob. 59AYUCh. 12.3 - Prob. 60AYUCh. 12.3 - Prob. 61AYUCh. 12.3 - Prob. 62AYUCh. 12.3 - Prob. 63AYUCh. 12.3 - Prob. 64AYUCh. 12.3 - Prob. 65AYUCh. 12.3 - Prob. 66AYUCh. 12.3 - Prob. 67AYUCh. 12.3 - Prob. 68AYUCh. 12.3 - Prob. 69AYUCh. 12.3 - Prob. 70AYUCh. 12.3 - Birthday Problem What is the probability that at...Ch. 12.3 - Birthday Problem What is the probability that at...Ch. 12.3 - Winning a Lottery: Powerball is a multistate...Ch. 12.3 - To graph , shift the graph of units and then ...Ch. 12.3 - Find the rectangular coordinates of the point...Ch. 12.3 - Solve: log 5 ( x+3 )=2Ch. 12.3 -
Ch. 12 - Prob. 1RECh. 12 - If , , and , find .
Ch. 12 - If n( A )=12 , n( AB )=30 , and n( AB )=6 , find...Ch. 12 - In Problems 4-9, use the information supplied in...Ch. 12 - In Problems 4-9, use the information supplied in...Ch. 12 - In Problems 4-9, use the information supplied in...Ch. 12 - In Problems 4-9, use the information supplied in...Ch. 12 - In Problems 4-9, use the information supplied in...Ch. 12 - In Problems 4-9, use the information supplied in...Ch. 12 - In Problems 10 and 11, compute the value of the...Ch. 12 - In Problems 10 and 11, compute the value of the...Ch. 12 - Stocking a Store A clothing store sells pure wool...Ch. 12 - Baseball On a given day, the American Baseball...Ch. 12 - Choosing Seats If 4 people enter a bus that has 9...Ch. 12 - Choosing a Team In how many ways can a squad of 4...Ch. 12 - Baseball In how many ways can 2 teams from 14...Ch. 12 - Telephone Numbers Using the digits 0, 1, 2,...,9,...Ch. 12 - License Plate Possibilities A license plate...Ch. 12 - Binary Codes Using the digits 0 and 1, how many...Ch. 12 - Arranging Flags How many different vertical...Ch. 12 - Forming Committees A group of 9 people is going to...Ch. 12 - Birthday Problem For this problem, assume that a...Ch. 12 - 23. Unemployment According to the U.S. Bureau of...Ch. 12 - You have four 1 bills, three 5 bills, and two 10...Ch. 12 - Each of the numbers 1, 2,..., 100 is written on an...Ch. 12 - At the Milex tune-up and brake repair shop, the...Ch. 12 - In Problems 14, a survey of 70college freshmen...Ch. 12 - In Problems 14, a survey of 70college freshmen...Ch. 12 - In Problems 14, a survey of 70college freshmen...Ch. 12 - In Problems 14, a survey of 70college freshmen...Ch. 12 - In Problems 57, compute the value of the given...Ch. 12 - In Problems 57, compute the value of the given...Ch. 12 - In Problems 57, compute the value of the given...Ch. 12 - MMs offers customers the opportunity to create...Ch. 12 - How many distinct 8-letter words (meaningful or...Ch. 12 - In horse racing, an exacta bet requires the bettor...Ch. 12 - In Ohio, license plates consist of three letters...Ch. 12 - Kiersten applies for admission to the University...Ch. 12 - A cooler contains 8 bottles of Pepsi, 5 bottles of...Ch. 12 - A study on the age distribution of students at a...Ch. 12 - In a certain lottery, there are ten balls numbered...Ch. 12 - If you roll die five times, what is the...Ch. 12 - Solve: 3x22x=1Ch. 12 - Graph f(x)=x2+4x5 by determining whether the graph...Ch. 12 - Graph f(x)=2(x+1)24 using transformations.Ch. 12 - Solve: |x4|0.01Ch. 12 - Find the complex zeros of f(x)=5x49x37x231x6Ch. 12 - Graph g(x)=3x1+5 using transformations. Find the...Ch. 12 - What is the exact value of log39?Ch. 12 - Solve: log2(3x2)+log2x=4Ch. 12 - Solve the system: {x2y+z=153x+y3z=82x+4yz=27Ch. 12 - What is the 33rd term in the sequence 3,1,5,9,...?...Ch. 12 - Graph: y=3sin(2x+)Ch. 12 - Prob. 12CR
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