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study help
mathematics
precalculus
Precalculus 9th edition Michael Sullivan - Solutions
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line.f(x) = -2x2 + x - 3 at (1, -4)
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line.f(x) = x2 - 2x +3 at (-1, 6)
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line.f(x) = 3x2 - x at (0, 0)
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line.f(x) = 2x2 + x at (1, 3)
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line.f(x) = -4x2 at (-2, -16)
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line.f(x) = 3x2 at (-1, 3)
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line.f(x) = 3 - x2 at (1, 2)
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line.f(x) = x2 + 2 at (-1, 3)
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line.f(x) = -2x + 1 at (-1, 3)
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line.f(x) = 3x + 5 at (1, 8)
True or False.The velocity of a particle whose position at time t is is s(t) the derivative s'(t).
True or False.The slope of the tangent line to the graph of f at (c, f(c)) is the derivative of f at c.
True or False.The tangent line to a function is the limiting position of a secant line.
If s = f(t) denotes the position of a particle at time t, the derivative f'(c) _______ is the of the particle at c.
If exists, it is called the______of at c. f(x) – f(c) lim
If exists, it equals the slope of the _______ to the graph of at the point (c, f(c)). f(x) – f(c) lim
True or False.The average rate of change of a function from a to b is f(b) + f(a) b + a
Find an equation of the line with slope 5 containing the point (2, -4).
Create a function that is not continuous at the number 5.
Name three functions that are continuous at every real number.
Use a graphing utility to graph the functions R given in Problem. Verify the solutions found above. x - 3x? + 4x – 12 x* - 3x + x – 3 R(x)
Use a graphing utility to graph the functions R given in Problem. Verify the solutions found above. .3 x + 2x2 + x R(x) 4 x* + x' + 2x + 2 .3
Use a graphing utility to graph the functions R given in Problem. Verify the solutions found above. x* - x + 3x – 3 R(x) x² + 3x – 4
Use a graphing utility to graph the functions R given in Problem. Verify the solutions found above. x - 2x2 + 4x – 8 ² + x – 6 R(x)
Use a graphing utility to graph the functions R given in Problem. Verify the solutions found above. x³ + x? + 3r + 3 R(x) x* + x + 2x + 2
Use a graphing utility to graph the functions R given in Problem. Verify the solutions found above. x3 - x + x – 1 R(x) x4 - x + 2r – 2
Determine where each rational function is undefined. Determine whether an asymptote or a hole appears at such numbers. x³ - x + 3x – 3 R(x) x² + 3x – 4
Determine where each rational function is undefined. Determine whether an asymptote or a hole appears at such numbers. x – 2x? + 4x – 8 ² + x – 6 R(x) %3D
Determine where each rational function is undefined. Determine whether an asymptote or a hole appears at such numbers. x* + 2x + x .4 .3 + x’ + 2x + 2 R(x)
Determine where each rational function is undefined. Determine whether an asymptote or a hole appears at such numbers. x3 - 3x? + 4x – 12 x* – 3x + x – 3 R(x)
Determine where each rational function is undefined. Determine whether an asymptote or a hole appears at such numbers. x³ + x² + 3x + 3 R(x) x* + x + 2x + 2
Determine where each rational function is undefined. Determine whether an asymptote or a hole appears at such numbers. x³ - x? + x – 1 R(x) x4 — х3 + 2х — 2
Discuss whether R is continuous at c. Use limits to analyze the graph of R at c. Graph R. c = -4 and c = 4 x? + 4x x² – 16 R(x)
Discuss whether R is continuous at c. Use limits to analyze the graph of R at c. Graph R. c = -1 and c = 1 x + x R(x) x – 1
Discuss whether R is continuous at c. Use limits to analyze the graph of R at c. Graph R. c = -2 and c = 2 3x + 6 x² – 4 R(x)
Discuss whether R is continuous at c. Use limits to analyze the graph of R at c. Graph R. c = -1 and c = 1 х — R(x) х2 — 1
Find the numbers at which is continuous. At which numbers is discontinuous? In x f(x) 3
Find the numbers at which is continuous. At which numbers is discontinuous? х f(x) : In x
Find the numbers at which is continuous. At which numbers is discontinuous? f(x) x? – 9
Find the numbers at which is continuous. At which numbers is discontinuous? 2х + 5 f(x) x² – 4
Find the numbers at which is continuous. At which numbers is discontinuous? f(x) = 4 cscx
Find the numbers at which is continuous. At which numbers is discontinuous? f(x) = 2 tanx
Find the numbers at which is continuous. At which numbers is discontinuous? f(x) = -2 cos x
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.1 + 2 + 22 + … + 2n-1 = 2n – 1
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.1 + 4 + 7 + ... + (3n - 2) = 1/2 n(3n - 1)
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.2 + 5 + 8 + ... + (3n - 1) = 1/2 n(3n + 1)
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.3 + 5 + 7 + ... + (2n + 1) = n(n + 2)
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.3 + 4 + 5 + ... + (n + 2) = 1/2 n(n + 5)
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.2 + 4 + 6 + ... + 2n = n(2n + 1)
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.2 + 4 + 6 + ... + 2n = n(n + 1)
Describe the similarities and differences between geometric sequences and exponential functions.
Make up a geometric sequence. Give it to a friend and ask for its 20th term.
Can a sequence be both arithmetic and geometric? Give reasons for your answer.
Suppose you were offered a job in which you would work 8 hours per day for 5 workdays per week for 1 month at hard manual labor. Your pay the first day would be 1 penny. On the second day your pay would be two pennies; the third day 4 pennies. Your pay would double on each successive workday. There
You have just signed a 7-year professional football league contract with a beginning salary of $2,000,000 per year. Management gives you the following options with regard to your salary over the 7 years. 1. A bonus of $100,000 each year 2. An annual increase of 4.5% per year beginning
Which of the following choices, A or B, results in more money? A: To receive $1000 on day 1, $999 on day 2, $998 on day 3, with the process to end after 1000 days B: To receive $1 on day 1, $2 on day 2, $4 on day 3, for 19 days
You are interviewing for a job and receive two offers: A: $20,000 to start, with guaranteed annual increases of 6% for the first 5 years B: $22,000 to start, with guaranteed annual increases of 3% for the first 5 years Which offer is better if your goal is to be making as much as
A rich man promises to give you $1000 on September 1, 2010. Each day thereafter he will give you 9/10 of what he gave you the previous day. What is the first date on which the amount you receive is less than 1¢? How much have you received when this happens?
Refer to Problem 99. Suppose that a stock pays an annual dividend of $2.50 and, historically, the dividend has increased 4% per year. You desire an annual rate of return of 11%. What is the most that you should pay for the stock?
One method of pricing a stock is to discount the stream of future dividends of the stock. Suppose that a stock pays per year in dividends and, historically, the dividend has been increased i% per year. If you desire an annual rate of return of r%, this method of pricing a stock states that the
Refer to Problem 97. Suppose that the marginal propensity to consume throughout the U.S. economy is 0.95. What is the multiplier for the U.S. economy?Problem 97Suppose that, throughout the U.S. economy, individuals spend 90% of every additional dollar that they earn. Economists would say that an
Suppose that, throughout the U.S. economy, individuals spend 90% of every additional dollar that they earn. Economists would say that an individual’s marginal propensity to consume is 0.90. For example, if Jane earns an additional dollar, she will spend of it. The individual that earns $0.90
Look at the figure. What fraction of the square is eventually shaded if the indicated shading process continues indefinitely?
In an old fable, a commoner who had saved the king’s life was told he could ask the king for any just reward. Being a shrewd man, the commoner said, “A simple wish, sire. Place one grain of wheat on the first square of a chessboard, two grains on the second square, four grains on the third
For a child born in 1996, the cost of a 4-year college education at a public university is projected to be $150,000. Assuming an 8% per annum rate of return compounded monthly, how much must be contributed to a college fund every month to have $150,000 in 18 years when the child begins college?
Scott and Alice want to purchase a vacation home in 10 years and need $50,000 for a down payment. How much should they place in a savings account each month if the per annum rate of return is assumed to be 6% compounded monthly?
Ray contributes $1000 to an Individual Retirement Account (IRA) semiannually. What will the value of the IRA be when Ray makes his 30th deposit (after 15 years) if the per annum rate of return is assumed to be 10% compounded semiannually?
Don contributes $500 at the end of each quarter to a tax-sheltered annuity (TSA).What will the value of the TSA be after the 80th deposit (20 years) if the per annum rate of return is assumed to be 8% compounded quarterly?
Jolene wants to purchase a new home. Suppose that she invests $400 per month into a mutual fund. If the per annum rate of return of the mutual fund is assumed to be 10% compounded monthly, how much will Jolene have for a down payment after the 36th deposit (3 years)?
Christine contributes $100 each month to her 401(k).What will be the value of Christine’s 401(k) after the 360th deposit (30 years) if the per annum rate of return is assumed to be 12% compounded monthly?
A ball is dropped from a height of 30 feet. Each time it strikes the ground, it bounces up to 0.8 of the previous height.
Initially, a pendulum swings through an arc of 2 feet. On each successive swing, the length of the arc is 0.9 of the previous length. (a) What is the length of the arc of the 10th swing? (b) On which swing is the length of the arc first less than 1 foot? (c) After 15 swings, what
A new piece of equipment cost a company $15,000. Each year, for tax purposes, the company depreciates the value by 15%. What value should the company give the equipment after 5 years?
If you have been hired at an annual salary of $18,000 and expect to receive annual increases of 5%, what will your salary be when you begin your fifth year?
Find x so that x - 1, x, and x + 2 are consecutive terms of a geometric sequence.
Find x so that x, x + 2 and x + 3 are are consecutive terms of a geometric sequence.
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. {(-1)n}
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. {3n/2}
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. 1, 1, 2, 3, 5, 8, ...
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. 1, 2, -4, 8, ...
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. п
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. п
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. 2, 4, 6, 8, ...
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. 1, 3, 6, 10, ...
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. 3 8. п 4.
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. 3 п 2.
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. {5n2 + 1}
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. {4n2}
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. {2n - 5}
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. {n + 2}
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 00 k 3 k=1
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 3 k=1
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. k-1 οο Σ- 4 k=1
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. k-1 ο0 Σ 6 3 k=1
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. k-1 3 Σ k=1
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 3k-1 2 k=1
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. k-1 ο0 Σε( 3 k=1
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. k-1 250 4 k=1
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 9 + 12 + 16 + 64/3 + ...
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 8 + 12 + 18 + 27 + ...
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