Applied Calculus
7th Edition
ISBN: 9781337291248
Author: Waner, Stefan.
Publisher: Cengage Learning,
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Chapter 1.3, Problem 8E
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The graph of
2(x² + y²)² = 25 (x²-y²), shown
in the figure, is a lemniscate of
Bernoulli. Find the equation of the
tangent line at the point (3,1).
-10
Write the expression for the slope in terms of x and y.
slope =
4x³ + 4xy2-25x
2
3
4x²y + 4y³ + 25y
Write the equation for the line tangent to the point (3,1).
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Chapter 1 Solutions
Applied Calculus
Ch. 1.1 - In Exercises 1-4, evaluate each expression based...Ch. 1.1 - In Exercises 1-4, evaluate each expression based...Ch. 1.1 - In Exercises 1-4, evaluate each expression based...Ch. 1.1 - In Exercises 1-4, evaluate each expression based...Ch. 1.1 - Prob. 5ECh. 1.1 - Prob. 6ECh. 1.1 - In Exercises 5-8, use the graph of the function f...Ch. 1.1 - Prob. 8ECh. 1.1 - In Exercises 9-12, say whether or not f(x) is...Ch. 1.1 - In Exercises 9-12, say whether or not f(x) is...
Ch. 1.1 - In Exercises 9-12, say whether or not f(x) is...Ch. 1.1 - Prob. 12ECh. 1.1 - Prob. 13ECh. 1.1 - Prob. 14ECh. 1.1 - Given f(x)=x2+2x+3, find a. f(0) b. f(1) c. f(1)...Ch. 1.1 - Prob. 16ECh. 1.1 - Given g(s)=s2+1s, find a. g(1) b. g(1) c. g(4) d....Ch. 1.1 - Prob. 18ECh. 1.1 - Prob. 19ECh. 1.1 - In Exercises 19-24, graph the given functions....Ch. 1.1 - Prob. 21ECh. 1.1 - Prob. 22ECh. 1.1 - Prob. 23ECh. 1.1 - Prob. 24ECh. 1.1 - In Exercises 25 and 26, match the functions to the...Ch. 1.1 - Prob. 26ECh. 1.1 - Prob. 27ECh. 1.1 - Prob. 28ECh. 1.1 - Prob. 29ECh. 1.1 - Prob. 30ECh. 1.1 - In Exercises 31-36, sketch the graph of the...Ch. 1.1 - In Exercises 31-36, sketch the graph of the...Ch. 1.1 - Prob. 33ECh. 1.1 - In Exercises 31-36, sketch the graph of the...Ch. 1.1 - In Exercises 31-36, sketch the graph of the...Ch. 1.1 - Prob. 36ECh. 1.1 - In Exercises 37-40, find and simplify (a)...Ch. 1.1 - Prob. 38ECh. 1.1 - Prob. 39ECh. 1.1 - In Exercises 37-40, find and simplify (a)...Ch. 1.1 - Prob. 41ECh. 1.1 - Offshore Crude Oil Production: Mexico The...Ch. 1.1 - Prob. 43ECh. 1.1 - Prob. 44ECh. 1.1 - Prob. 45ECh. 1.1 - Prob. 46ECh. 1.1 - Housing Starts Exercises 45-48 refer to the...Ch. 1.1 - Prob. 48ECh. 1.1 - Prob. 49ECh. 1.1 - Prob. 50ECh. 1.1 - Net Income: Casual Apparel In the following graph,...Ch. 1.1 - Net Income: Casual Apparel In the following graph,...Ch. 1.1 - Funding for NASA: 1958-1966 The percentage of the...Ch. 1.1 - Funding for NASA: 1966-2015 The percentage of the...Ch. 1.1 - Acquisition of Language The percentage p(t) of...Ch. 1.1 - Acquisition of Language The percentage p(t)...Ch. 1.1 - Processor Speeds The processor speed, in megahertz...Ch. 1.1 - Prob. 58ECh. 1.1 - Prob. 59ECh. 1.1 - Prob. 60ECh. 1.1 - Prob. 61ECh. 1.1 - Prob. 62ECh. 1.1 - Complete the following: The function notation for...Ch. 1.1 - Prob. 64ECh. 1.1 - Prob. 65ECh. 1.1 - Prob. 66ECh. 1.1 - Prob. 67ECh. 1.1 - Prob. 68ECh. 1.1 - Prob. 69ECh. 1.1 - Prob. 70ECh. 1.1 - Prob. 71ECh. 1.1 - Why is the following assertion false? If f(2)=2...Ch. 1.1 - Prob. 73ECh. 1.1 - Prob. 74ECh. 1.1 - Prob. 75ECh. 1.1 - How do the graphs of two functions f and g differ...Ch. 1.2 - Exercises 1-8 are based on the following...Ch. 1.2 - Exercises 1-8 are based on the following...Ch. 1.2 - Exercises 1-8 are based on the following...Ch. 1.2 - Prob. 4ECh. 1.2 - Exercises 1-8 are based on the following...Ch. 1.2 - Prob. 6ECh. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Resources You now have 200 music files on your...Ch. 1.2 - Resources The amount of free space left on your...Ch. 1.2 - Soccer My rectangular soccer field site has a...Ch. 1.2 - Cabbage My rectangular cabbage patch has a total...Ch. 1.2 - Vegetables I want to fence in a square vegetable...Ch. 1.2 - Orchids My square orchid garden abuts my house so...Ch. 1.2 - Study You study math 4 hours a day on Sunday...Ch. 1.2 - Recreation You spend 5 hours per day on Saturdays...Ch. 1.2 - Prob. 17ECh. 1.2 - Cost The cost of renting tuxes for the Choral...Ch. 1.2 - Break-Even Analysis Your college newspaper, The...Ch. 1.2 - Break-Even Analysis The Audubon Society at...Ch. 1.2 - Break-Even Analysis Gymnast Clothing manufactures...Ch. 1.2 - Break-Even Analysis Gymnast Clothing also...Ch. 1.2 - Break-Even Analysis: School Construction Costs The...Ch. 1.2 - Break-Even Analysis: School Construction Costs The...Ch. 1.2 - Profit Analysis: Aviation The hourly operating...Ch. 1.2 - Prob. 26ECh. 1.2 - Break-Even Analysis (based on a question from a...Ch. 1.2 - Prob. 28ECh. 1.2 - Break-Even Analysis (from a CPA exam) Given the...Ch. 1.2 - Prob. 30ECh. 1.2 - Break-Even Analysis: Organized Crime The organized...Ch. 1.2 - Break-Even Analysis: Disorganized Crime Butch...Ch. 1.2 - Prob. 33ECh. 1.2 - Prob. 34ECh. 1.2 - Demand: Smartphones The worldwide demand for...Ch. 1.2 - Demand: Smartphones (See Exercise 35.) Here is...Ch. 1.2 - Equilibrium Price: Skateboards The demand for your...Ch. 1.2 - Equilibrium Price: Skateboards The demand for your...Ch. 1.2 - Equilibrium Price: Cell Phones Worldwide quarterly...Ch. 1.2 - Equilibrium Price: Cell Phones Worldwide annual...Ch. 1.2 - Demand: E-Readers The demand for Amuons Kindle...Ch. 1.2 - Prob. 42ECh. 1.2 - Prob. 43ECh. 1.2 - Prob. 44ECh. 1.2 - Spending on Corrections in the 1990s The following...Ch. 1.2 - Spending on Corrections in the 1990s Repeat...Ch. 1.2 - Prob. 47ECh. 1.2 - Prob. 48ECh. 1.2 - Prob. 49ECh. 1.2 - Prob. 50ECh. 1.2 - Prob. 51ECh. 1.2 - Social Website Popularity: Twitter The following...Ch. 1.2 - Prob. 53ECh. 1.2 - Prob. 54ECh. 1.2 - Investments In August 2013, E*TRADE Financial was...Ch. 1.2 - Prob. 56ECh. 1.2 - Prob. 57ECh. 1.2 - Prob. 58ECh. 1.2 - Prob. 59ECh. 1.2 - Prob. 60ECh. 1.2 - Prob. 61ECh. 1.2 - Prob. 62ECh. 1.2 - Prob. 63ECh. 1.2 - Iodine Decay The amount of iodine 131 remaining in...Ch. 1.2 - Prob. 65ECh. 1.2 - Prob. 66ECh. 1.2 - Prob. 67ECh. 1.2 - Prob. 68ECh. 1.2 - Fill in the missing information for the following...Ch. 1.2 - Prob. 70ECh. 1.2 - Prob. 71ECh. 1.2 - Prob. 72ECh. 1.2 - Prob. 73ECh. 1.2 - Prob. 74ECh. 1.2 - Prob. 75ECh. 1.2 - Prob. 76ECh. 1.2 - Prob. 77ECh. 1.2 - If f and g are functions with f(x)g(x)0 for every...Ch. 1.2 - Prob. 79ECh. 1.2 - Prob. 80ECh. 1.3 - In Exercises 1-6, a table of values for a linear...Ch. 1.3 - Prob. 2ECh. 1.3 - In Exercises 1-6, a table of values for a linear...Ch. 1.3 - Prob. 4ECh. 1.3 - Prob. 5ECh. 1.3 - Prob. 6ECh. 1.3 - In Exercises 7-10, first find f(0), if not...Ch. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - Prob. 10ECh. 1.3 - In Exercises 11-14, decide which of the two given...Ch. 1.3 - In Exercises 11-14, decide which of the two given...Ch. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - In Exercises 15-24, find the slope of the given...Ch. 1.3 - In Exercises 15-24, find the slope of the given...Ch. 1.3 - In Exercises 15-24, find the slope of the given...Ch. 1.3 - In Exercises 15-24, find the slope of the given...Ch. 1.3 - In Exercises 15-24, find the slope of the given...Ch. 1.3 - In Exercises 15-24, find the slope of the given...Ch. 1.3 - In Exercises 15-24, find the slope of the given...Ch. 1.3 - In Exercises 15-24, find the slope of the given...Ch. 1.3 - In Exercises 2538, graph the given equation.[HINT:...Ch. 1.3 - Prob. 26ECh. 1.3 - Prob. 27ECh. 1.3 - Prob. 28ECh. 1.3 - Prob. 29ECh. 1.3 - Prob. 30ECh. 1.3 - Prob. 31ECh. 1.3 - In Exercises 2538, graph the given equation.[HINT:...Ch. 1.3 - In Exercises 2538, graph the given equation.[HINT:...Ch. 1.3 - In Exercises 2538, graph the given equation.[HINT:...Ch. 1.3 - In Exercises 2538, graph the given equation.[HINT:...Ch. 1.3 - In Exercises 2538, graph the given equation.[HINT:...Ch. 1.3 - Prob. 37ECh. 1.3 - Prob. 38ECh. 1.3 - Prob. 39ECh. 1.3 - Prob. 40ECh. 1.3 - Prob. 41ECh. 1.3 - Prob. 42ECh. 1.3 - In Exercises 39-58, calculate the exact slope...Ch. 1.3 - Prob. 44ECh. 1.3 - Prob. 45ECh. 1.3 - In Exercises 39-58, calculate the exact slope...Ch. 1.3 - Prob. 47ECh. 1.3 - Prob. 48ECh. 1.3 - Prob. 49ECh. 1.3 - Prob. 50ECh. 1.3 - Prob. 51ECh. 1.3 - Prob. 52ECh. 1.3 - In Exercises 39-58, calculate the exact slope...Ch. 1.3 - In Exercises 39-58, calculate the exact slope...Ch. 1.3 - In Exercises 39-58, calculate the exact slope...Ch. 1.3 - In Exercises 39-58, calculate the exact slope...Ch. 1.3 - In Exercises 39-58, calculate the exact slope...Ch. 1.3 - In Exercises 39-58, calculate the exact slope...Ch. 1.3 - In the following figure, estimate the slopes of...Ch. 1.3 - In the following figure, estimate the slopes of...Ch. 1.3 - In Exercises 61-80, find a linear equation whose...Ch. 1.3 - In Exercises 61-80, find a linear equation whose...Ch. 1.3 - In Exercises 61-80, find a linear equation whose...Ch. 1.3 - In Exercises 61-80, find a linear equation whose...Ch. 1.3 - In Exercises 61-80, find a linear equation whose...Ch. 1.3 - In Exercises 61-80, find a linear equation whose...Ch. 1.3 - In Exercises 61-80, find a linear equation whose...Ch. 1.3 - Prob. 68ECh. 1.3 - Prob. 69ECh. 1.3 - Prob. 70ECh. 1.3 - In Exercises 61-80, find a linear equation whose...Ch. 1.3 - In Exercises 61-80, find a linear equation whose...Ch. 1.3 - Prob. 73ECh. 1.3 - Prob. 74ECh. 1.3 - Prob. 75ECh. 1.3 - Prob. 76ECh. 1.3 - Prob. 77ECh. 1.3 - Prob. 78ECh. 1.3 - Prob. 79ECh. 1.3 - In Exercises 61-80, find a linear equation whose...Ch. 1.3 - Prob. 81ECh. 1.3 - Cost A soft-drink manufacturer can produce 1,000...Ch. 1.3 - Cost: iPhone 5 (16 GB) If it costs Apple $2,070 to...Ch. 1.3 - Cost: Kinects If it costs Microsoft $1,230 to...Ch. 1.3 - Demand Sales figures show that your company sold...Ch. 1.3 - Demand A large department store is prepared to buy...Ch. 1.3 - Demand for Smartphones The following table shows...Ch. 1.3 - Demand for Smartphones The following table shows...Ch. 1.3 - Demand for Monorail Service: Las Vegas In 2005 the...Ch. 1.3 - Demand/or Monorail Service: Mars The Utarek...Ch. 1.3 - Pasta Imports in the 1990s During the period...Ch. 1.3 - Prob. 92ECh. 1.3 - Net Income The net income of Amazon decreased from...Ch. 1.3 - Operating Expenses The operating expenses of...Ch. 1.3 - Velocity The position of a model train, in feet...Ch. 1.3 - Velocity The height of a falling sheet of paper,...Ch. 1.3 - Fast Cars A police car was traveling down Ocean...Ch. 1.3 - Prob. 98ECh. 1.3 - Textbook Sizes The second edition of Applied...Ch. 1.3 - Textbook Sizes The second edition of Finite...Ch. 1.3 - Prob. 101ECh. 1.3 - Prob. 102ECh. 1.3 - Prob. 103ECh. 1.3 - Prob. 104ECh. 1.3 - Prob. 105ECh. 1.3 - Prob. 106ECh. 1.3 - Processor Speeds The processor speed, in megahertz...Ch. 1.3 - Processor Speeds The processor speed, in megahertz...Ch. 1.3 - Superbowl Advertising Exercises 109 and 110 are...Ch. 1.3 - Prob. 110ECh. 1.3 - Employment in Mexico The number of workers...Ch. 1.3 - Mortgage Delinquencies The percentage of borrowers...Ch. 1.3 - Prob. 113ECh. 1.3 - Prob. 114ECh. 1.3 - Prob. 115ECh. 1.3 - Prob. 116ECh. 1.3 - Prob. 117ECh. 1.3 - Suppose that y is decreasing at a rate of 4 units...Ch. 1.3 - Prob. 119ECh. 1.3 - Prob. 120ECh. 1.3 - Prob. 121ECh. 1.3 - Prob. 122ECh. 1.3 - Prob. 123ECh. 1.3 - Prob. 124ECh. 1.3 - Prob. 125ECh. 1.3 - Prob. 126ECh. 1.3 - Prob. 127ECh. 1.3 - Prob. 128ECh. 1.3 - Prob. 129ECh. 1.3 - Prob. 130ECh. 1.3 - Prob. 131ECh. 1.3 - Prob. 132ECh. 1.3 - Suppose the cost function is C(x)=mx+b (with m and...Ch. 1.3 - You have been constructing a demand equation, and...Ch. 1.4 - Prob. 1ECh. 1.4 - Prob. 2ECh. 1.4 - Prob. 3ECh. 1.4 - Prob. 4ECh. 1.4 - Prob. 5ECh. 1.4 - Prob. 6ECh. 1.4 - Prob. 7ECh. 1.4 - In Exercises 5-8, use technology to compute the...Ch. 1.4 - Prob. 9ECh. 1.4 - Prob. 10ECh. 1.4 - Prob. 11ECh. 1.4 - Prob. 12ECh. 1.4 - Prob. 13ECh. 1.4 - Prob. 14ECh. 1.4 - Mobile Broadband Subscriptions The following table...Ch. 1.4 - Fixed-Line Telephone Subscriptions The following...Ch. 1.4 - Demand for Smartphones The following table shows...Ch. 1.4 - Demand for Smartphones The following table shows...Ch. 1.4 - Oil Recovery The Texas Bureau of Economic Geology...Ch. 1.4 - Oil Recovery (Refer to Exercise 19.) The following...Ch. 1.4 - Profit: Amazon The following table shows Amazons...Ch. 1.4 - Prob. 22ECh. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - Soybean Production: Cerrados The following table...Ch. 1.4 - Prob. 26ECh. 1.4 - Prob. 27ECh. 1.4 - Prob. 28ECh. 1.4 - Prob. 29ECh. 1.4 - Doctorates in Mexico Exercises 29-32 are based on...Ch. 1.4 - Prob. 31ECh. 1.4 - Doctorates in Mexico Exercises 29-32 are based on...Ch. 1.4 - Prob. 33ECh. 1.4 - Prob. 34ECh. 1.4 - Prob. 35ECh. 1.4 - Prob. 36ECh. 1.4 - Prob. 37ECh. 1.4 - Prob. 38ECh. 1.4 - If the points (x1,x1),(x2,y2),,(xn,yn) lie on a...Ch. 1.4 - Prob. 40ECh. 1.4 - Prob. 41ECh. 1.4 - Prob. 42ECh. 1.4 - Prob. 43ECh. 1.4 - Prob. 44ECh. 1.4 - Prob. 45ECh. 1.4 - Prob. 46ECh. 1 - In Exercises 1-4, use the graph of the function f...Ch. 1 - Prob. 2RECh. 1 - Prob. 3RECh. 1 - Prob. 4RECh. 1 - Prob. 5RECh. 1 - Prob. 6RECh. 1 - Prob. 7RECh. 1 - Prob. 8RECh. 1 - In Exercises 9-14, decide whether the specified...Ch. 1 - Prob. 10RECh. 1 - Prob. 11RECh. 1 - Prob. 12RECh. 1 - Prob. 13RECh. 1 - Prob. 14RECh. 1 - In Exercises 15-22, find the equation of the...Ch. 1 - In Exercises 15-22, find the equation of the...Ch. 1 - In Exercises 15-22, find the equation of the...Ch. 1 - In Exercises 15-22, find the equation of the...Ch. 1 - In Exercises 15-22, find the equation of the...Ch. 1 - In Exercises 15-22, find the equation of the...Ch. 1 - In Exercises 15-22, find the equation of the...Ch. 1 - Prob. 22RECh. 1 - Prob. 23RECh. 1 - Prob. 24RECh. 1 - Prob. 25RECh. 1 - Prob. 26RECh. 1 - Prob. 27RECh. 1 - Prob. 28RECh. 1 - Website Stability John OHagan is considering...Ch. 1 - Book Sales As OHaganBooks.com has grown in...Ch. 1 - Prob. 31RECh. 1 - Prob. 32RECh. 1 - Prob. 33RECh. 1 - Prob. 34RECh. 1 - Prob. 35RECh. 1 - Prob. 36RECh. 1 - Recreation John OHagan has just returned from a...Ch. 1 - Crickets The mountain retreat near Puerto Vallarta...Ch. 1 - Break-Even Analysis OHaganBooks.com has recently...Ch. 1 - Break-Even Analysis OHaganBooks.com also generates...Ch. 1 - Demand and Profit To generate a profit from its...Ch. 1 - Demand and Profit To generate a profit from its...Ch. 1 - Prob. 43RECh. 1 - Prob. 44RE
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