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![Given that f(x) = M-x². wier series of the function f(x)=0-22, NE [-II] Converges to { { f(-+ +0) + f(-0)} 5 [14 f(-07%) + 4](http://img.homeworklib.com/questions/c25592b0-a99d-11ea-b4c7-bf565e3540c3.png?x-oss-process=image/resize,w_560)
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1. (pp. 592, Marsden & Hoffman) For each of the functions determine what type of convergence...
3. (pp. 592, Marsden & Hoffman] Suppose that f:1-1, 1] → R is differentiable on (–,],...
3. (pp. 592, Marsden & Hoffman] Suppose that f:1-1, 1] → R is differentiable on (–,], f(-1) = f (TT), and f' and f" are sectionally continuous, with jump discontinuities. Show that a L 15()dx = Ž** (% +6%), T J - n=1 where an, bn are the Fourier coefficients of f. Use Schwarz's inequality to show that the number series -1 (a2 + 6%)"/2 converges.
1. (6 points- 3 points each) Determine the radius of convergence and the interval of convergence ...
1. (6 points- 3 points each) Determine the radius of convergence
and the interval of convergence for each series listed below:
(a) ∞ (−1)n(2x − 4)2n n=1 n3n
(b) ∞ (x−7)n2n
1. (6 point- 3 points each) Determine the radius of convergence and the interval of rgence for each series listed below: (a) Σ (-1)-(2x-4)2n 2 conve n3n n-1 3n2
1. (6 point- 3 points each) Determine the radius of convergence and the interval of rgence for each series listed...
(d) f(x) = (1 + x) ln(1 + x) Hint: differentiate. (4) Expand the following functions...
(d) f(x) = (1 + x) ln(1 + x) Hint: differentiate. (4) Expand the following functions into power series centered at 0 and find the radius of convergence. You can either use geometric series method, known expansions, or derivatives. You don't have to analyze the remainder.
solve for a and b 1. Plot each of the following functions and find its Fourier series representation, also determine...
solve for a and b
1. Plot each of the following functions and find its Fourier series representation, also determine the first three One zero harmonics (a) f(t) -1<t< T= 2 where T is the period. 0t<1 J (b) f(t) -t-1<t<0 T 4 where T is the poriod = 0t1 0-2<t<-1 T = 4 where T is the period (e) g(t) 1 -1<t<1 0 1<t<2 (d) g(t) = 1- t -1<t<1;T = 4 where T is the period
1. Plot...
1 Problem 7 We know that we can expand as a power series for -1 <...
1 Problem 7 We know that we can expand as a power series for -1 < < 1. 1+2 Follow the given steps to manipulate this power series to derive the power series representation for f(x) = tan-(2) centered at a = 0. • Make the appropriate substitution to find a power series for g(x) 1/(1 + x2). • Either integrate or differentiate the previous power series to find a power series for f(x) = tan-'(x). Has the radius of...
Fourier Series for Odd Functions Recall that if f is an odd function, f(-x)f(x). An odd Fourier series has only the...
Fourier Series for Odd Functions Recall that if f is an odd function, f(-x)f(x). An odd Fourier series has only the sine terms, and can be approximate an odd function, so Fo(x) b sinx)+b2 sin(2x)+ b, sin(3x)+. Why is there no b, term in the series F, (x)? 1. 2. Using steps similar to those outlined for even functions, develop a rule for finding the coefficients to approximate any odd function on the interval [-π, π]. 3. If f (x)sin...
5. Determine the convergence of the series: 1 V11 - 4 V11 + 4 V13-4 1...
5. Determine the convergence of the series: 1 V11 - 4 V11 + 4 V13-4 1 1 1 + 1 13+ 4 + 1 15 + 4 +.. 15-4 6. A rod with length L is lying in the x-axis, with one of its edge is located at the origin. According to the Newton's law of gravity, if the density of the rod is 1 and Newton's constant is then the gravitational field at the point C = (A, B)...
7. Determine the radius of convergence and the interval of convergence for the power series: (-1)"+1"...
7. Determine the radius of convergence and the interval of convergence for the power series: (-1)"+1" n2 nxn b. An=1 > C. X- + 3! 5! 8. A probability density function f(x) is an important concept in statistical sciences. It gives you the distribution of the random variable x. f(x) usually defined in a certain interval, and vanish in the rest. One can defined the median j and variances oas using the probability density function as (you'll see more about...
determine which answer to put by saying the answer is A,b,c or d and what to...
determine which answer to put by saying the answer is A,b,c or d
and what to write in the two boxes below
This Question: 1 pt Consider the function f(x)=5 tan -(x). a. Differentiate the Taylor series about for f(x). b. Identify the function represented by the differentiated series. c. Give the interval of convergence of the power series for the derivative. a. Choose the correct answer below. O A. 25** - 25x^4 + 25x24 - 25x34 + O B....
(a) What kind of functions can be decomposed into Fourier series and what 10 into Fourier...
(a) What kind of functions can be decomposed into Fourier series and what 10 into Fourier integral? man (b) When analysing stability of equilibrium states in various physical prob- lems, why do we suppose variations about equilibrium values to be Small? (c) In which physical problems do we come across Bessel's equations (men- tion one or two problems commenting on symmetry properties of solu- tions)? (d) When solving the wave or heat equation by separation of variables, we first seek...
3. (pp. 592, Marsden & Hoffman] Suppose that f:1-1, 1] → R is differentiable on (–,], f(-1) = f (TT), and f' and f" are sectionally continuous, with jump discontinuities. Show that a L 15()dx = Ž** (% +6%), T J - n=1 where an, bn are the Fourier coefficients of f. Use Schwarz's inequality to show that the number series -1 (a2 + 6%)"/2 converges.
1. (6 points- 3 points each) Determine the radius of convergence
and the interval of convergence for each series listed below:
(a) ∞ (−1)n(2x − 4)2n n=1 n3n
(b) ∞ (x−7)n2n
1. (6 point- 3 points each) Determine the radius of convergence and the interval of rgence for each series listed below: (a) Σ (-1)-(2x-4)2n 2 conve n3n n-1 3n2
1. (6 point- 3 points each) Determine the radius of convergence and the interval of rgence for each series listed...
(d) f(x) = (1 + x) ln(1 + x) Hint: differentiate. (4) Expand the following functions into power series centered at 0 and find the radius of convergence. You can either use geometric series method, known expansions, or derivatives. You don't have to analyze the remainder.
solve for a and b
1. Plot each of the following functions and find its Fourier series representation, also determine the first three One zero harmonics (a) f(t) -1<t< T= 2 where T is the period. 0t<1 J (b) f(t) -t-1<t<0 T 4 where T is the poriod = 0t1 0-2<t<-1 T = 4 where T is the period (e) g(t) 1 -1<t<1 0 1<t<2 (d) g(t) = 1- t -1<t<1;T = 4 where T is the period
1. Plot...
1 Problem 7 We know that we can expand as a power series for -1 < < 1. 1+2 Follow the given steps to manipulate this power series to derive the power series representation for f(x) = tan-(2) centered at a = 0. • Make the appropriate substitution to find a power series for g(x) 1/(1 + x2). • Either integrate or differentiate the previous power series to find a power series for f(x) = tan-'(x). Has the radius of...
Fourier Series for Odd Functions Recall that if f is an odd function, f(-x)f(x). An odd Fourier series has only the sine terms, and can be approximate an odd function, so Fo(x) b sinx)+b2 sin(2x)+ b, sin(3x)+. Why is there no b, term in the series F, (x)? 1. 2. Using steps similar to those outlined for even functions, develop a rule for finding the coefficients to approximate any odd function on the interval [-π, π]. 3. If f (x)sin...
5. Determine the convergence of the series: 1 V11 - 4 V11 + 4 V13-4 1 1 1 + 1 13+ 4 + 1 15 + 4 +.. 15-4 6. A rod with length L is lying in the x-axis, with one of its edge is located at the origin. According to the Newton's law of gravity, if the density of the rod is 1 and Newton's constant is then the gravitational field at the point C = (A, B)...
7. Determine the radius of convergence and the interval of convergence for the power series: (-1)"+1" n2 nxn b. An=1 > C. X- + 3! 5! 8. A probability density function f(x) is an important concept in statistical sciences. It gives you the distribution of the random variable x. f(x) usually defined in a certain interval, and vanish in the rest. One can defined the median j and variances oas using the probability density function as (you'll see more about...
determine which answer to put by saying the answer is A,b,c or d
and what to write in the two boxes below
This Question: 1 pt Consider the function f(x)=5 tan -(x). a. Differentiate the Taylor series about for f(x). b. Identify the function represented by the differentiated series. c. Give the interval of convergence of the power series for the derivative. a. Choose the correct answer below. O A. 25** - 25x^4 + 25x24 - 25x34 + O B....
(a) What kind of functions can be decomposed into Fourier series and what 10 into Fourier integral? man (b) When analysing stability of equilibrium states in various physical prob- lems, why do we suppose variations about equilibrium values to be Small? (c) In which physical problems do we come across Bessel's equations (men- tion one or two problems commenting on symmetry properties of solu- tions)? (d) When solving the wave or heat equation by separation of variables, we first seek...
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