Calculus with Applications (11th Edition)
11th Edition
ISBN: 9780321979421
Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Publisher: PEARSON
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Chapter 12, Problem 13RE
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A body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.
A chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as:
dx/dt = k(a-x)(b-x)
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Consider a body of mass m dropped from rest at t = 0. The body falls under the influence of gravity, and the air resistance FD opposing the motion is assumed to be proportional to the square of the velocity, so that FD = kV2. Call x the vertical distance and take the positive direction of the x-axis downward, with origin at the initial position of the body. Obtain relationships for the velocity and position of the body as a function of time t.
Chapter 12 Solutions
Calculus with Applications (11th Edition)
Ch. 12.1 - Find the first four terms of the sequence having...Ch. 12.1 - Prob. 2YTCh. 12.1 - Prob. 3YTCh. 12.1 - Prob. 4YTCh. 12.1 - Prob. 5YTCh. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - List the first n terms of the geometric sequence...Ch. 12.1 - Prob. 5E
Ch. 12.1 - List the first n terms of the geometric sequence...Ch. 12.1 - Find a5 and an for the following geometric...Ch. 12.1 - Find a5 and an for the following geometric...Ch. 12.1 - Find a5 and an for the following geometric...Ch. 12.1 - Prob. 10ECh. 12.1 - Find a5 and an for the following geometric...Ch. 12.1 - Prob. 12ECh. 12.1 - Prob. 13ECh. 12.1 - Find a5 and an for the following geometric...Ch. 12.1 - For each sequence that is geometric, find r and...Ch. 12.1 - For each sequence that is geometric, find r and...Ch. 12.1 - For each sequence that is geometric, find r and...Ch. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - For each sequence that is geometric, find r and...Ch. 12.1 - For each sequence that is geometric, find r and...Ch. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Find the sum of the first five terms of each...Ch. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Find the sum of the first five terms of each...Ch. 12.1 - Find the sum of the first five terms of each...Ch. 12.1 - Prob. 29ECh. 12.1 - Prob. 30ECh. 12.1 - Prob. 31ECh. 12.1 - Use the formula for the sum of the first n terms...Ch. 12.1 - Prob. 33ECh. 12.1 - Prob. 34ECh. 12.1 - Prob. 35ECh. 12.1 - Use the formula for the sum of the first n terms...Ch. 12.1 - Prob. 37ECh. 12.1 - Use the formula for the sum of the first n terms...Ch. 12.1 - Prob. 39ECh. 12.1 - Income An oil well produced $4,000,000 of income...Ch. 12.1 - Savings Suppose you could save $1 on January 1, $2...Ch. 12.1 - Depreciation Each year a machine loses 30% of the...Ch. 12.1 - Population The population of a certain colony of...Ch. 12.1 - Radioactive Decay The half-life of a radioactive...Ch. 12.1 - Rotation of a Wheel A bicycle wheel rotates 400...Ch. 12.1 - Thickness of a Paper Stack A piece of paper is...Ch. 12.1 - Prob. 47ECh. 12.1 - Game Shows Some game shows sponsor tournaments...Ch. 12.2 - EXAMPLE 1 Annuity
Erin D’Aquanni is an athlete who...Ch. 12.2 - Prob. 2YTCh. 12.2 - Prob. 3YTCh. 12.2 - Prob. 4YTCh. 12.2 - Prob. 5YTCh. 12.2 - Prob. 6YTCh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Find the amount of each ordinary annuity....Ch. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Find the amount of each ordinary annuity based on...Ch. 12.2 - Prob. 10ECh. 12.2 - Prob. 11ECh. 12.2 - Prob. 12ECh. 12.2 - Prob. 13ECh. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Find the present value of each ordinary...Ch. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.2 - Prob. 23ECh. 12.2 - Find the lump sum deposited today that will yield...Ch. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - Prob. 27ECh. 12.2 - Prob. 28ECh. 12.2 - Prob. 29ECh. 12.2 - Prob. 30ECh. 12.2 - Amount of an Annuity Sarah Shepherd wants to...Ch. 12.2 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Prob. 35ECh. 12.2 - Prob. 36ECh. 12.2 - Individual Retirement Accounts With Individual...Ch. 12.2 - Prob. 38ECh. 12.2 - Prob. 39ECh. 12.2 - Prob. 40ECh. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - Investment In 1995, Oseola McCarty donated...Ch. 12.2 - Prob. 44ECh. 12.2 - Present Value of an Annuity In his will the late...Ch. 12.2 - Prob. 46ECh. 12.2 - Lottery Winnings In most states, the winnings of...Ch. 12.2 - Prob. 48ECh. 12.2 - Prob. 49ECh. 12.2 - Prob. 50ECh. 12.2 - Prob. 51ECh. 12.2 - Prob. 52ECh. 12.2 - Prob. 53ECh. 12.2 - Prob. 54ECh. 12.2 - Prob. 55ECh. 12.2 - Amortization Certain large semitrailer trucks cost...Ch. 12.2 - Prob. 57ECh. 12.2 - Prob. 58ECh. 12.3 - Use a Taylor polynomial of degree 5 to approximate...Ch. 12.3 - Prob. 2YTCh. 12.3 - Prob. 3YTCh. 12.3 - Prob. 1WECh. 12.3 - Prob. 2WECh. 12.3 - Prob. 3WECh. 12.3 - Prob. 4WECh. 12.3 - For the functions defined as follows, find the...Ch. 12.3 - For the functions defined as follows, find the...Ch. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Prob. 6ECh. 12.3 - For the functions defined as follows, find the...Ch. 12.3 - For the functions defined as follows, find the...Ch. 12.3 - Prob. 9ECh. 12.3 - Prob. 10ECh. 12.3 - For the functions defined as follows, find the...Ch. 12.3 - Prob. 12ECh. 12.3 - For the functions defined as follows, find the...Ch. 12.3 - For the functions defined as follows, find the...Ch. 12.3 - For the functions defined as follows, find the...Ch. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - For the functions defined as follows, find the...Ch. 12.3 - For the functions defined as follows, find the...Ch. 12.3 - Prob. 20ECh. 12.3 - Prob. 21ECh. 12.3 - Prob. 22ECh. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Prob. 25ECh. 12.3 - Prob. 26ECh. 12.3 - Prob. 27ECh. 12.3 - Use Taylor polynomials of degree 4 at x = 0, found...Ch. 12.3 - Use Taylor polynomials of degree 4 at x = 0, found...Ch. 12.3 - Prob. 30ECh. 12.3 - Use Taylor polynomials of degree 4 at x = 0, found...Ch. 12.3 - Use Taylor polynomials of degree 4 at x = 0, found...Ch. 12.3 - Use Taylor polynomials of degree 4 at x = 0, found...Ch. 12.3 - Use Taylor polynomials of degree 4 at x = 0, found...Ch. 12.3 - Find a polynomial of degree 3 such that f(0) = 3,...Ch. 12.3 - Find a polynomial of degree 4 such that f(0) = 1,...Ch. 12.3 - Generalize the result of Example 2 to show that if...Ch. 12.3 - Duration Let D represent duration, a term in...Ch. 12.3 - APPLY IT Replacement Time for a Part A book on...Ch. 12.3 - In Exercises 40–44, use a Taylor polynomial of...Ch. 12.3 - Prob. 41ECh. 12.3 - In Exercises 40–44, use a Taylor polynomial of...Ch. 12.3 - In Exercises 40–44, use a Taylor polynomial of...Ch. 12.3 - In Exercises 40–44, use a Taylor polynomial of...Ch. 12.3 - Species Survival According to a text on species...Ch. 12.3 - Prob. 46ECh. 12.4 - Find the first five partial sums for the sequence...Ch. 12.4 - Prob. 2YTCh. 12.4 - Prob. 3YTCh. 12.4 - Identify which geometric series converge. Give the...Ch. 12.4 - Identify which geometric series converge. Give the...Ch. 12.4 - Identify which geometric series converge. Give the...Ch. 12.4 - Identify which geometric series converge. Give the...Ch. 12.4 - Identify which geometric series converge. Give the...Ch. 12.4 - Identify which geometric series converge. Give the...Ch. 12.4 - Identify which geometric series converge. Give the...Ch. 12.4 - Identify which geometric series converge. Give the...Ch. 12.4 - Identify which geometric series converge. Give the...Ch. 12.4 - Identify which geometric series converge. Give the...Ch. 12.4 - Identify which geometric series converge. Give the...Ch. 12.4 - Identify which geometric series converge. Give the...Ch. 12.4 - Identify which geometric series converge. Give the...Ch. 12.4 - Identify which geometric series converge. Give the...Ch. 12.4 - The nth term of a sequence is given. Calculate the...Ch. 12.4 - The nth term of a sequence is given. Calculate the...Ch. 12.4 - The nth term of a sequence is given. Calculate the...Ch. 12.4 - The nth term of a sequence is given. Calculate the...Ch. 12.4 - The nth term of a sequence is given. Calculate the...Ch. 12.4 - The nth term of a sequence is given. Calculate the...Ch. 12.4 - The repeating decimal 0.222222 … can be expressed...Ch. 12.4 - The repeating decimal 0. 18181818 … can be...Ch. 12.4 - The following classical formulas for computing the...Ch. 12.4 - Production Orders A sugar factory receives an...Ch. 12.4 - Tax Rebate The government claims to be able to...Ch. 12.4 - Present Value In Section 8.3, we computed the...Ch. 12.4 - Malpractice Insurance An insurance company...Ch. 12.4 - Automobile Insurance In modeling the number of...Ch. 12.4 - Prob. 29ECh. 12.4 - Prob. 30ECh. 12.4 - Prob. 31ECh. 12.4 - Perimeter A sequence of equilateral triangles is...Ch. 12.4 - Prob. 33ECh. 12.4 - Trains Suppose a train leaves a station at noon...Ch. 12.4 - Zeno’s Paradox In the fifth century b.c., the...Ch. 12.4 - Prob. 36ECh. 12.4 - Sports In sports such as squash, played using...Ch. 12.5 - Prob. 1YTCh. 12.5 - Prob. 2YTCh. 12.5 - Prob. 3YTCh. 12.5 - Find the Taylor series for the functions defined...Ch. 12.5 - Prob. 2ECh. 12.5 - Prob. 3ECh. 12.5 - Prob. 4ECh. 12.5 - Prob. 5ECh. 12.5 - Prob. 6ECh. 12.5 - Find the Taylor series for the functions defined...Ch. 12.5 - Find the Taylor series for the functions defined...Ch. 12.5 - Prob. 9ECh. 12.5 - Prob. 10ECh. 12.5 - Prob. 11ECh. 12.5 - Find the Taylor series for the functions defined...Ch. 12.5 - Prob. 13ECh. 12.5 - Prob. 14ECh. 12.5 - Prob. 15ECh. 12.5 - Prob. 16ECh. 12.5 - Prob. 17ECh. 12.5 - Prob. 18ECh. 12.5 - Prob. 19ECh. 12.5 - Prob. 20ECh. 12.5 - Prob. 21ECh. 12.5 - Prob. 22ECh. 12.5 - Use the fact that
to find a Taylor series for (1...Ch. 12.5 - Prob. 24ECh. 12.5 - Prob. 25ECh. 12.5 - Prob. 26ECh. 12.5 - Prob. 27ECh. 12.5 - Prob. 28ECh. 12.5 - Prob. 29ECh. 12.5 - Prob. 30ECh. 12.5 - Prob. 31ECh. 12.5 - Prob. 32ECh. 12.5 - Prob. 33ECh. 12.5 - Prob. 34ECh. 12.5 - Business and Economics
Investment Tim Wilson has...Ch. 12.5 - Prob. 36ECh. 12.5 - Infant Mortality Infant mortality is an example of...Ch. 12.5 - Prob. 38ECh. 12.5 - Prob. 39ECh. 12.6 - Prob. 1YTCh. 12.6 - Prob. 2YTCh. 12.6 - Prob. 1WECh. 12.6 - Prob. 2WECh. 12.6 - Use Newton’s method to find a solution for each...Ch. 12.6 - Use Newton’s method to find a solution for each...Ch. 12.6 - Prob. 3ECh. 12.6 - Use Newton’s method to find a solution for each...Ch. 12.6 - Prob. 5ECh. 12.6 - Prob. 6ECh. 12.6 - Prob. 7ECh. 12.6 - Prob. 8ECh. 12.6 - Prob. 9ECh. 12.6 - Prob. 10ECh. 12.6 - Use Newton’s method to find a solution for each...Ch. 12.6 - Prob. 12ECh. 12.6 - Prob. 13ECh. 12.6 - Prob. 14ECh. 12.6 - Use Newton’s method to find a solution for each...Ch. 12.6 - Prob. 16ECh. 12.6 - Use Newton’s method to find each root to the...Ch. 12.6 - Prob. 18ECh. 12.6 - Use Newton’s method to find each root to the...Ch. 12.6 - Prob. 20ECh. 12.6 - Prob. 21ECh. 12.6 - Use Newton’s method to find each root to the...Ch. 12.6 - Prob. 23ECh. 12.6 - Prob. 24ECh. 12.6 - Use Newton’s method to find each root to the...Ch. 12.6 - Prob. 26ECh. 12.6 - Prob. 27ECh. 12.6 - Use Newton’s method to find the critical points...Ch. 12.6 - Prob. 29ECh. 12.6 - Prob. 30ECh. 12.6 - Use Newton’s method to attempt to find a solution...Ch. 12.6 - Break-Even Point For a particular product, the...Ch. 12.6 - Manufacturing A new manufacturing process produces...Ch. 12.6 - Prob. 34ECh. 12.6 - Prob. 35ECh. 12.6 - Prob. 36ECh. 12.7 - Prob. 1YTCh. 12.7 - Prob. 2YTCh. 12.7 - Prob. 3YTCh. 12.7 - Prob. 4YTCh. 12.7 - Prob. 5YTCh. 12.7 - Prob. 6YTCh. 12.7 - Prob. 1WECh. 12.7 - Prob. 2WECh. 12.7 - Use lHospitals rule where applicable to find each...Ch. 12.7 - Prob. 2ECh. 12.7 - Prob. 3ECh. 12.7 - Prob. 4ECh. 12.7 - Prob. 5ECh. 12.7 - Prob. 6ECh. 12.7 - Prob. 7ECh. 12.7 - Prob. 8ECh. 12.7 - Prob. 9ECh. 12.7 - Prob. 10ECh. 12.7 - Prob. 11ECh. 12.7 - Prob. 12ECh. 12.7 - Prob. 13ECh. 12.7 - Prob. 14ECh. 12.7 - Prob. 15ECh. 12.7 - Prob. 16ECh. 12.7 - Prob. 17ECh. 12.7 - Prob. 18ECh. 12.7 - Prob. 19ECh. 12.7 - Prob. 20ECh. 12.7 - Prob. 21ECh. 12.7 - Prob. 22ECh. 12.7 - Prob. 23ECh. 12.7 - Prob. 24ECh. 12.7 - Prob. 25ECh. 12.7 - Prob. 26ECh. 12.7 - Prob. 27ECh. 12.7 - Prob. 28ECh. 12.7 - Prob. 29ECh. 12.7 - Prob. 30ECh. 12.7 - Prob. 31ECh. 12.7 - Prob. 32ECh. 12.7 - Prob. 33ECh. 12.7 - Prob. 34ECh. 12.7 - Prob. 35ECh. 12.7 - Prob. 36ECh. 12.7 - Prob. 37ECh. 12.7 - Prob. 38ECh. 12.7 - Prob. 39ECh. 12.7 - Prob. 40ECh. 12.7 - Prob. 41ECh. 12.7 - Prob. 42ECh. 12.7 - Prob. 43ECh. 12.7 - Prob. 44ECh. 12.7 - Prob. 45ECh. 12.7 - Prob. 46ECh. 12.7 - Prob. 47ECh. 12.7 - Prob. 48ECh. 12.7 - Prob. 49ECh. 12 - Prob. 1RECh. 12 - Prob. 2RECh. 12 - Prob. 3RECh. 12 - Prob. 4RECh. 12 - Prob. 5RECh. 12 - Prob. 6RECh. 12 - Prob. 7RECh. 12 - Prob. 8RECh. 12 - Prob. 9RECh. 12 - Prob. 10RECh. 12 - Prob. 11RECh. 12 - Prob. 12RECh. 12 - Prob. 13RECh. 12 - Prob. 14RECh. 12 - Prob. 15RECh. 12 - Prob. 16RECh. 12 - Prob. 17RECh. 12 - Prob. 18RECh. 12 - Prob. 19RECh. 12 - Prob. 20RECh. 12 - Prob. 21RECh. 12 - Prob. 22RECh. 12 - Prob. 23RECh. 12 - Prob. 24RECh. 12 - Prob. 25RECh. 12 - Prob. 26RECh. 12 - Prob. 27RECh. 12 - Prob. 28RECh. 12 - Prob. 29RECh. 12 - Prob. 30RECh. 12 - Prob. 31RECh. 12 - Prob. 32RECh. 12 - Prob. 33RECh. 12 - Prob. 34RECh. 12 - Prob. 35RECh. 12 - Prob. 36RECh. 12 - Prob. 37RECh. 12 - Prob. 38RECh. 12 - Prob. 39RECh. 12 - Prob. 40RECh. 12 - Prob. 41RECh. 12 - Prob. 42RECh. 12 - Prob. 43RECh. 12 - Prob. 44RECh. 12 - Prob. 45RECh. 12 - Prob. 46RECh. 12 - Prob. 47RECh. 12 - Prob. 48RECh. 12 - Prob. 49RECh. 12 - Prob. 50RECh. 12 - Prob. 51RECh. 12 - Prob. 52RECh. 12 - Prob. 53RECh. 12 - Prob. 54RECh. 12 - Prob. 55RECh. 12 - Prob. 56RECh. 12 - Prob. 57RECh. 12 - Prob. 58RECh. 12 - Prob. 59RECh. 12 - Prob. 60RECh. 12 - Prob. 61RECh. 12 - Prob. 62RECh. 12 - Prob. 63RECh. 12 - Prob. 64RECh. 12 - Prob. 65RECh. 12 - Prob. 66RECh. 12 - Prob. 67RECh. 12 - Prob. 68RECh. 12 - Prob. 69RECh. 12 - Prob. 70RECh. 12 - Prob. 71RECh. 12 - Prob. 72RECh. 12 - Prob. 73RECh. 12 - Prob. 74RECh. 12 - Prob. 75RECh. 12 - Prob. 76RECh. 12 - Prob. 77RECh. 12 - Prob. 78RECh. 12 - Prob. 79RECh. 12 - Prob. 80RECh. 12 - Prob. 81RECh. 12 - Prob. 82RECh. 12 - Prob. 83RECh. 12 - Prob. 84RECh. 12 - Prob. 85RECh. 12 - Prob. 86RE
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