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mathematics
precalculus

Questions and Answers of Precalculus

Find the derivative of each function at the given number. f(x) = x2 – 3 at 0
Find the derivative of each function at the given number. f(x) = -4 + 3x at 1
Find the derivative of each function at the given number. f(x) = -4x + 5 at 3
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line.f(x) = x3 - x2 at (1, 0)
Find the slope of the tangent line to the graph of at the given point. Graph and the tangent line.f(x) = x3 + x at (2, 10)
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
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
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,
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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

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