Calculus Volume 2
2nd Edition
ISBN: 9781630182021
Author: Gilbert Strang, Edwin Jed Herman
Publisher: OpenStax College.
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Textbook Question
Chapter 6.3, Problem 146E
In the following exercises, find the Taylor series of the given function centered at the indicated point.
146. exat a = −1
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What is a solution to a differential equation? We said that a differential equation is an equation that
describes the derivative, or derivatives, of a function that is unknown to us. By a solution to a differential
equation, we mean simply a function that satisfies this description.
2. Here is a differential equation which describes an unknown position function s(t):
ds
dt
318
4t+1,
ds
(a) To check that s(t) = 2t2 + t is a solution to this differential equation, calculate
you really do get 4t +1.
and check that
dt'
(b) Is s(t) = 2t2 +++ 4 also a solution to this differential equation?
(c) Is s(t)=2t2 + 3t also a solution to this differential equation?
ds
1
dt
(d) To find all possible solutions, start with the differential equation = 4t + 1, then move dt to the
right side of the equation by multiplying, and then integrate both sides. What do you get?
(e) Does this differential equation have a unique solution, or an infinite family of solutions?
these are solutions to a tutorial that was done and im a little lost. can someone please explain to me how these iterations function, for example i Do not know how each set of matrices produces a number if someine could explain how its done and provide steps it would be greatly appreciated thanks.
Chapter 6 Solutions
Calculus Volume 2
Ch. 6.1 - In the following exercises, state whether each...Ch. 6.1 - In the following exercises, state whether each...Ch. 6.1 - In the following exercises, state whether each...Ch. 6.1 - In the following exercises, state whether each...Ch. 6.1 - In the following exercises, state whether each...Ch. 6.1 - In the following exercises, state whether each...Ch. 6.1 - In the following exercises, suppose that |an+1an|1...Ch. 6.1 - In the following exercises, suppose that |an+1an|1...Ch. 6.1 - In the following exercises, suppose that |an+1an|1...Ch. 6.1 - In the following exercises, suppose that |an+1an|1...
Ch. 6.1 - In the following exercises, suppose that |an+1an|1...Ch. 6.1 - In the following exercises, suppose that |an+1an|1...Ch. 6.1 - In the following exercises, find the radius of...Ch. 6.1 - In the following exercises, find the radius of...Ch. 6.1 - In the following exercises, find the radius of...Ch. 6.1 - In the following exercises, find the radius of...Ch. 6.1 - In the following exercises, find the radius of...Ch. 6.1 - In the following exercises, find the radius of...Ch. 6.1 - In the following exercises, find the radius of...Ch. 6.1 - In the following exercises, find the radius of...Ch. 6.1 - In the following exercises, find the radius of...Ch. 6.1 - In the following exercises, find the radius of...Ch. 6.1 - In the following exercises, find the radius of...Ch. 6.1 - In the following exercises, find the radius of...Ch. 6.1 - In the following exercises, find the radius of...Ch. 6.1 - In the following exercises, find the radius of...Ch. 6.1 - In the following exercises, find the radius of...Ch. 6.1 - In the following exercises, find the radius of...Ch. 6.1 - In the following exercises, use the ratio test to...Ch. 6.1 - In the following exercises, use the ratio test to...Ch. 6.1 - In the following exercises, use the ratio test to...Ch. 6.1 - In the following exercises, use the ratio test to...Ch. 6.1 - In the following exercises, given that 11x=n=0xn...Ch. 6.1 - In the following exercises, given that 11x=n=0xn...Ch. 6.1 - In the following exercises, given that 11x=n=0xn...Ch. 6.1 - In the following exercises, given that 11x=n=0xn...Ch. 6.1 - In the following exercises, given that 11x=n=0xn...Ch. 6.1 - In the following exercises, given that 11x=n=0xn...Ch. 6.1 - In the following exercises, given that 11x=n=0xn...Ch. 6.1 - In the following exercises, given that 11x=n=0xn...Ch. 6.1 - In the following exercises, given that 11x=n=0xn...Ch. 6.1 - In the following exercises, given that 11x=n=0xn...Ch. 6.1 - Use the next exercise to find the radius of...Ch. 6.1 - Use the next exercise to find the radius of...Ch. 6.1 - Use the next exercise to find the radius of...Ch. 6.1 - Use the next exercise to find the radius of...Ch. 6.1 - Use the next exercise to find the radius of...Ch. 6.1 - Use the next exercise to find the radius of...Ch. 6.1 - Use the next exercise to find the radius of...Ch. 6.1 - Use the next exercise to find the radius of...Ch. 6.1 - Use the next exercise to find the radius of...Ch. 6.1 - In the following exercises, suppose that p(x)=...Ch. 6.1 - In the following exercises, suppose that...Ch. 6.1 - In the following exercises, suppose that...Ch. 6.1 - In the following exercises, suppose that...Ch. 6.1 - In the following exercises, suppose that...Ch. 6.1 - In the following exercises, suppose that...Ch. 6.1 - In the following exercises, suppose that...Ch. 6.1 - In the following exercises, suppose that...Ch. 6.1 - In the following exercises, suppose that...Ch. 6.1 - In the following exercises, suppose that...Ch. 6.1 - In the following exercises, suppose that...Ch. 6.2 - If f(x)=n=0xnn! and g(x)=n=0(1)nxnn! , find the...Ch. 6.2 - If C(x)=n=0x2n(2n)! and S(x)=n=0x2n+1(2n+1)! find...Ch. 6.2 - In the following exercises, use partial fractions...Ch. 6.2 - In the following exercises, use partial fractions...Ch. 6.2 - In the following exercises, use partial fractions...Ch. 6.2 - In the following exercises, use partial fractions...Ch. 6.2 - In the following exercises, express each series as...Ch. 6.2 - In the following exercises, express each series as...Ch. 6.2 - In the following exercises, express each series as...Ch. 6.2 - In the following exercises, express each series as...Ch. 6.2 - The following exercises explore applications of...Ch. 6.2 - The following exercises explore applications of...Ch. 6.2 - The following exercises explore applications of...Ch. 6.2 - The following exercises explore applications of...Ch. 6.2 - The following exercises explore applications of...Ch. 6.2 - The following exercises explore applications of...Ch. 6.2 - In the following exercises, express the sum of...Ch. 6.2 - In the following exercises, express the sum of...Ch. 6.2 - In the following exercises, express the sum of...Ch. 6.2 - In the following exercises, express the sum of...Ch. 6.2 - In the following exercises, find the power series...Ch. 6.2 - In the following exercises, find the power series...Ch. 6.2 - In the following exercises, find the power series...Ch. 6.2 - In the following exercises, find the power series...Ch. 6.2 - In the following exercises, differentiate the...Ch. 6.2 - In the following exercises, differentiate the...Ch. 6.2 - In the following exercises, integrate the given...Ch. 6.2 - In the following exercises, integrate the given...Ch. 6.2 - In the following exercises, evaluate each infinite...Ch. 6.2 - In the following exercises, evaluate each infinite...Ch. 6.2 - In the following exercises, evaluate each infinite...Ch. 6.2 - In the following exercises, evaluate each infinite...Ch. 6.2 - In the following exercises, given that 11x=n=0xn...Ch. 6.2 - In the following exercises, given that 11x=n=0xn...Ch. 6.2 - In the following exercises, given that 11x=n=0xn...Ch. 6.2 - In the following exercises, given that 11x=n=0xn...Ch. 6.2 - In the following exercises, given that 11x=n=0xn...Ch. 6.2 - In the following exercises, given that 11x=n=0xn...Ch. 6.2 - In the following exercises, given that 11x=n=0xn...Ch. 6.2 - T] Evaluate the power series expansion ln(1 + x) =...Ch. 6.2 - [T] Subtract the infinite series of 1n(1 x) from...Ch. 6.2 - In the following exercises, using a substitution...Ch. 6.2 - In the following exercises, using a substitution...Ch. 6.2 - In the following exercises, using a substitution...Ch. 6.2 - In the following exercises, using a substitution...Ch. 6.2 - In the following exercises, using a substitution...Ch. 6.2 - In the following exercises, using a substitution...Ch. 6.2 - In the following exercises, using a substitution...Ch. 6.2 - In the following exercises, using a substitution...Ch. 6.2 - In the following exercises, using a substitution...Ch. 6.2 - In the following exercises, using a substitution...Ch. 6.2 - In the following exercises, using a substitution...Ch. 6.2 - In the following exercises, using a substitution...Ch. 6.3 - In this project. we use the Macburin polynomials...Ch. 6.3 - In this project. we use the Macburin polynomials...Ch. 6.3 - In this project. we use the Macburin polynomials...Ch. 6.3 - In this project. we use the Macburin polynomials...Ch. 6.3 - In this project. we use the Macburin polynomials...Ch. 6.3 - In this project. we use the Macburin polynomials...Ch. 6.3 - In the following exercises, find the Taylor...Ch. 6.3 - In the following exercises, find the Taylor...Ch. 6.3 - In the following exercises, find the Taylor...Ch. 6.3 - In the following exercises, find the Taylor...Ch. 6.3 - In the following exercises, find the Taylor...Ch. 6.3 - In the following exercises, find the Taylor...Ch. 6.3 - In the following exercises, find the Taylor...Ch. 6.3 - In the following exercises, find the Taylor...Ch. 6.3 - In the following exercises, verify that the given...Ch. 6.3 - In the following exercises, verify that the given...Ch. 6.3 - In the following exercises, verify that the given...Ch. 6.3 - In the following exercises, verify that the given...Ch. 6.3 - In the following exercises, verify that the given...Ch. 6.3 - In the following exercises, verify that the given...Ch. 6.3 - In the following exercises, verify that the given...Ch. 6.3 - In the following exercises, verify that the given...Ch. 6.3 - In the following exercises, find the smallest...Ch. 6.3 - In the following exercises, find the smallest...Ch. 6.3 - In the following exercises, find the smallest...Ch. 6.3 - In the following exercises, find the smallest...Ch. 6.3 - In the following exercises, the maximum of the...Ch. 6.3 - In the following exercises, the maximum of the...Ch. 6.3 - In the following exercises, the maximum of the...Ch. 6.3 - In the following exercises, the maximum of the...Ch. 6.3 - In the following exercises, find the Taylor series...Ch. 6.3 - In the following exercises, find the Taylor series...Ch. 6.3 - In the following exercises, find the Taylor series...Ch. 6.3 - In the following exercises, find the Taylor series...Ch. 6.3 - In the following exercises, find the Taylor series...Ch. 6.3 - In the following exercises, find the Taylor series...Ch. 6.3 - In the following exercises, find the Taylor series...Ch. 6.3 - In the following exercises, find the Taylor series...Ch. 6.3 - In the following exercises, find the Taylor series...Ch. 6.3 - In the following exercises, find the Taylor series...Ch. 6.3 - In the following exercises, find the Taylor series...Ch. 6.3 - In the following exercises, compute the Taylor...Ch. 6.3 - In the following exercises, compute the Taylor...Ch. 6.3 - In the following exercises, compute the Taylor...Ch. 6.3 - In the following exercises, compute the Taylor...Ch. 6.3 - In the following exercises, compute the Taylor...Ch. 6.3 - In the following exercises, compute the Taylor...Ch. 6.3 - In the following exercises, compute the Taylor...Ch. 6.3 - In the following exercises, compute the Taylor...Ch. 6.3 - In the following exercises, compute the Taylor...Ch. 6.3 - [T] In the following exercises, identify the value...Ch. 6.3 - [T] In the following exercises, identify the value...Ch. 6.3 - [T] In the following exercises, identify the value...Ch. 6.3 - [T] In the following exercises, identify the value...Ch. 6.3 - The following exercises make use of the functions...Ch. 6.3 - The following exercises make use of the functions...Ch. 6.3 - The following exercises make use of the functions...Ch. 6.3 - The following exercises make use of the functions...Ch. 6.3 - The following exercises make use of the functions...Ch. 6.3 - The following exercises make use of the functions...Ch. 6.3 - In the following exercises, use the fact that if...Ch. 6.3 - In the following exercises, use the fact that if...Ch. 6.3 - In the following exercises, use the fact that if...Ch. 6.3 - In the following exercises, use the fact that if...Ch. 6.4 - In the following exercises, use appropriate...Ch. 6.4 - In the following exercises, use appropriate...Ch. 6.4 - In the following exercises, use appropriate...Ch. 6.4 - In the following exercises, use appropriate...Ch. 6.4 - In the following exercises, use the substitution...Ch. 6.4 - In the following exercises, use the substitution...Ch. 6.4 - In the following exercises, use the substitution...Ch. 6.4 - In the following exercises, use the substitution...Ch. 6.4 - In the following exercises, use the substitution...Ch. 6.4 - In the following exercises, use the substitution...Ch. 6.4 - In the following exercises, use the substitution...Ch. 6.4 - In the following exercises, use the substitution...Ch. 6.4 - In the following exercises, use the binomial...Ch. 6.4 - In the following exercises, use the binomial...Ch. 6.4 - In the following exercises, use the binomial...Ch. 6.4 - In the following exercises, use the binomial...Ch. 6.4 - In the following exercises, use the binomial...Ch. 6.4 - In the following exercises, use the binomial...Ch. 6.4 - In the following exercises, use the binomial...Ch. 6.4 - In the following exercises, use the binomial...Ch. 6.4 - In the following exercises, use the expansion...Ch. 6.4 - In the following exercises, use the expansion...Ch. 6.4 - In the following exercises, use the expansion...Ch. 6.4 - In the following exercises, use the expansion...Ch. 6.4 - In the following exercises, use the expansion...Ch. 6.4 - In the following exercises, use the expansion...Ch. 6.4 - In the following exercises, use the expansion...Ch. 6.4 - In the following exercises, use the expansion...Ch. 6.4 - In the following exercises, find the Maclaurin...Ch. 6.4 - In the following exercises, find the Maclaurin...Ch. 6.4 - In the following exercises, find the Maclaurin...Ch. 6.4 - In the following exercises, find the Maclaurin...Ch. 6.4 - In the following exercises, find the Maclaurin...Ch. 6.4 - In the following exercises, find the Maclaurin...Ch. 6.4 - In the following exercises, find the Maclaurin...Ch. 6.4 - In the following exercises, find the Maclaurin...Ch. 6.4 - In the following exercises, find the Maclaurin...Ch. 6.4 - In the following exercises, find the Maclaurin...Ch. 6.4 - In the following exercises, find the Maclaurin...Ch. 6.4 - In the following exercises, find the Maclaurin...Ch. 6.4 - In the following exercises, find the Maclaurin...Ch. 6.4 - In the following exercises, find the Maclaurin...Ch. 6.4 - In the following exercises, find the Maclaurin...Ch. 6.4 - In the following exercises, find the Maclaurin...Ch. 6.4 - In the following exercises, compute at least the...Ch. 6.4 - In the following exercises, compute at least the...Ch. 6.4 - In the following exercises, compute at least the...Ch. 6.4 - In the following exercises, compute at least the...Ch. 6.4 - In the following exercises, compute at least the...Ch. 6.4 - In the following exercises, compute at least the...Ch. 6.4 - In the following exercises, compute at least the...Ch. 6.4 - In the following exercises, compute at least the...Ch. 6.4 - In the following exercises, find the radius of...Ch. 6.4 - In the following exercises, find the radius of...Ch. 6.4 - In the following exercises, find the radius of...Ch. 6.4 - In the following exercises, find the radius of...Ch. 6.4 - In the following exercises, find the radius of...Ch. 6.4 - In the following exercises, find the radius of...Ch. 6.4 - In the following exercises, find the radius of...Ch. 6.4 - 233. [T] Let Sn(s)=k=0n(1)kx 2k+1(2k+1)! and...Ch. 6.4 - Use the identity 2 sin x cos x = sin (2x) to find...Ch. 6.4 - If y=n=0anxn , find the power series expansions of...Ch. 6.4 - [T] Suppose that y=k=0akxk satisfies y'=-2xy and...Ch. 6.4 - [T] Suppose that a set of standardized test scores...Ch. 6.4 - [T] Suppose that a set of standardized test scores...Ch. 6.4 - [T] Suppose that n=0anxn converges to a function...Ch. 6.4 - [T] Suppose that n=0anxn converges to a function...Ch. 6.4 - Suppose that n=0anxn converges to a function y...Ch. 6.4 - Suppose that n=0anxnconverges to a function y such...Ch. 6.4 - [T] 0sinttdt;Ps=1 x 23!+ x 45!+ x 67!+ x 89! may...Ch. 6.4 - [T] t;P11=1x2+x42+x63!+....x2211! May assume that...Ch. 6.4 - The following exercises deal with Fresnel...Ch. 6.4 - The following exercises deal with Fresnel...Ch. 6.4 - The following exercises deal with Fresnel...Ch. 6.4 - The following exercises deal with Fresnel...Ch. 6.4 - The following exercises deal with Fresnel...Ch. 6.4 - The following exercises deal with Fresnel...Ch. 6.4 - The following exercises deal with Fresnel...Ch. 6.4 - The following exercises deal with Fresnel...Ch. 6 - True or False? In the following exercises, justify...Ch. 6 - True or False? In the following exercises, justify...Ch. 6 - True or False? In the following exercises, justify...Ch. 6 - True or False? In the following exercises, justify...Ch. 6 - In the following exercises, find the radius of...Ch. 6 - In the following exercises, find the radius of...Ch. 6 - In the following exercises, find the radius of...Ch. 6 - In the following exercises, find the radius of...Ch. 6 - In the following exercises, find the power series...Ch. 6 - In the following exercises, find the power series...Ch. 6 - In the following exercises, find the power series...Ch. 6 - In the following exercises, find the power series...Ch. 6 - In the following exercises, evaluate the Taylor...Ch. 6 - In the following exercises, evaluate the Taylor...Ch. 6 - In the following exercises, find the Maclaurin...Ch. 6 - In the following exercises, find the Maclaurin...Ch. 6 - In the following exercises, find the Taylor series...Ch. 6 - In the following exercises, find the Taylor series...Ch. 6 - In the following exercises, find the Maclaurin...Ch. 6 - In the following exercises, find the Maclaurin...Ch. 6 - In the following exercises, find the Maclaurin...Ch. 6 - In the following exercises, find the Maclaurin...Ch. 6 - In the following exercises, find the Maclaurin...Ch. 6 - The following exercises consider problems of...Ch. 6 - The following exercises consider problems of...Ch. 6 - The following exercises consider problems of...
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