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3. At the beginning of 8.6, we investigated the graph of f(x) = ? and the...
1 point) Consider the Fourier series: nTTc a. Find the Fourier coefficients for the function f(x) 1.2 an b. Use the computer to draw the Fourier series of f(a), for x E[-18, 18], showing clearly all...
1 point) Consider the Fourier series: nTTc a. Find the Fourier coefficients for the function f(x) 1.2 an b. Use the computer to draw the Fourier series of f(a), for x E[-18, 18], showing clearly all points of convergence. Also, show the graphs with the partial sums of the Fourier series using n5 and n20 terms. What do you observe?
1 point) Consider the Fourier series: nTTc a. Find the Fourier coefficients for the function f(x) 1.2 an b. Use...
(1 point) Consider the Fourier sine series: ) 14, sin( f(z) a. Find the Fourier coefficients for the function f(x)-9, 0, TL b. Use the computer to draw the Fourier sine series of f(x), for x E-15, 15...
(1 point) Consider the Fourier sine series: ) 14, sin( f(z) a. Find the Fourier coefficients for the function f(x)-9, 0, TL b. Use the computer to draw the Fourier sine series of f(x), for x E-15, 151, showing clearly all points of convergence. Also, show the graphs with the partial sums of the Fourier series using n = 5 and n = 20 terms.
(1 point) Consider the Fourier sine series: ) 14, sin( f(z) a. Find the Fourier...
(1 point) Find the first five non-zero terms of power series representation centered at x = 0 for the function below. f(x) = arctan(3) Answer: f(x) = + 0 1 /4 What is the radius of convergence? Answe...
(1 point) Find the first five non-zero terms of power series representation centered at x = 0 for the function below. f(x) = arctan(3) Answer: f(x) = + 0 1 /4 What is the radius of convergence? Answer: R= 4
(1 point) Find the first five non-zero terms of power series representation centered at x = 0 for the function below. f(x) = arctan(3) Answer: f(x) = + 0 1 /4 What is the radius of convergence? Answer: R= 4
Ex. 3.9. Develop Fourier-Legendre series for f(x) = sin(21x). Graph on common axes the partial sums...
Ex. 3.9. Develop Fourier-Legendre series for f(x) = sin(21x). Graph on common axes the partial sums Sm, m = 1,2, ...,M up to that SM whose graph visually coincides with that of f(x) within the graphical accuracy. State the value of M you determined and list the exact values of all expansion coefficients from ao to am. Hint: to solve this problem you need to use one of the available sym- bolic algebra packages MAPLE or MATHEMATICA to evaluate the...
3) Later in this course, we will learn that the function, arctan x, is equivalent to a power series for x on the interval -1sxs: 2n+1 (-1)" arctan x = We can use this power series to approxim...
3) Later in this course, we will learn that the function, arctan x, is equivalent to a power series for x on the interval -1sxs: 2n+1 (-1)" arctan x = We can use this power series to approximate the constant π . a) First, evaluate arctan1). (You do not need the series to evaluate it.) b) Use your answer from part (a) and the power series above to find a series representation for (The answer will be just a series-not...
k for 2 5. Consider the function f(x) = 37T 0 for 2 Hint: See examples...
k for 2 5. Consider the function f(x) = 37T 0 for 2 Hint: See examples of functions of a generic period t; James, 4th ed. pg. 581, Ex. 7.7 & 7.8 (a) State wether it has even or odd symmetry (b) Find the Fourier series representation for f. Plot graphs of the first three partial sums SI (c) Using the result in part (b), show that 1 + 1 +.. 7 4
k for 2 5. Consider the function...
1. Let f(1) = ***+3. (a) (3 points) Sketch the region S below the graph of...
1. Let f(1) = ***+3. (a) (3 points) Sketch the region S below the graph of y = f(x) and between x = 0 and * = 4. Remember to label axes and important points! (b) (4 points) Approximate the area A of the region S using rectangles by dividing (0,4into four equal subintervals and creating rectangles with the right endpoints. Here you will be calculating R4. It may help to draw the rectangles on your graph (c) (2 points)...
15. Let f(x) = 2 . 2+x a) Find the power series representation of f(x) centered at o b) Use the power series representation to find ½ dx. 16. Find the Taylor Series for f(x) = sin (2x) centered a...
15. Let f(x) = 2 . 2+x a) Find the power series representation of f(x) centered at o b) Use the power series representation to find ½ dx. 16. Find the Taylor Series for f(x) = sin (2x) centered at T.
15. Let f(x) = 2 . 2+x a) Find the power series representation of f(x) centered at o b) Use the power series representation to find ½ dx. 16. Find the Taylor Series for f(x) = sin (2x) centered...
Question 4 10 pts #3. Consider the function f(x) = 2 3 (a) (5pts) Find a...
Question 4 10 pts #3. Consider the function f(x) = 2 3 (a) (5pts) Find a power series for f(x) centered at 0. (b) (5pts) Determine the interval of convergence of f(x). Upload Choose a File Question 5 10 pts #4. (a) (5pts) Find the Taylor series for f(x) = cos x, centered at 0. (Note: You can refer to the textbook.) (b) (5pts) Using (a), find the Maclaurin series for g(x) = cos(a). Write the first five terms of...
Consider the graph 12 10 6, 9) y-f(x 8 (2, 7) (4, 5) (0, 3) (8, 0) 10 (a) Using the indicated subintervals, approximate the shaded area by using lower sums s (rectangles that lie below the graph of f...
Consider the graph 12 10 6, 9) y-f(x 8 (2, 7) (4, 5) (0, 3) (8, 0) 10 (a) Using the indicated subintervals, approximate the shaded area by using lower sums s (rectangles that lie below the graph of f) (b) Using the indicated subintervals, approximate the shaded area by using upper sums S (rectangles that extend above the graph of f) +-14 points SullivanCalc1 5.1.019 Approximate the area A under the graph of function f from a to b...
1 point) Consider the Fourier series: nTTc a. Find the Fourier coefficients for the function f(x) 1.2 an b. Use the computer to draw the Fourier series of f(a), for x E[-18, 18], showing clearly all points of convergence. Also, show the graphs with the partial sums of the Fourier series using n5 and n20 terms. What do you observe?
1 point) Consider the Fourier series: nTTc a. Find the Fourier coefficients for the function f(x) 1.2 an b. Use...
(1 point) Consider the Fourier sine series: ) 14, sin( f(z) a. Find the Fourier coefficients for the function f(x)-9, 0, TL b. Use the computer to draw the Fourier sine series of f(x), for x E-15, 151, showing clearly all points of convergence. Also, show the graphs with the partial sums of the Fourier series using n = 5 and n = 20 terms.
(1 point) Consider the Fourier sine series: ) 14, sin( f(z) a. Find the Fourier...
(1 point) Find the first five non-zero terms of power series representation centered at x = 0 for the function below. f(x) = arctan(3) Answer: f(x) = + 0 1 /4 What is the radius of convergence? Answer: R= 4
(1 point) Find the first five non-zero terms of power series representation centered at x = 0 for the function below. f(x) = arctan(3) Answer: f(x) = + 0 1 /4 What is the radius of convergence? Answer: R= 4
Ex. 3.9. Develop Fourier-Legendre series for f(x) = sin(21x). Graph on common axes the partial sums Sm, m = 1,2, ...,M up to that SM whose graph visually coincides with that of f(x) within the graphical accuracy. State the value of M you determined and list the exact values of all expansion coefficients from ao to am. Hint: to solve this problem you need to use one of the available sym- bolic algebra packages MAPLE or MATHEMATICA to evaluate the...
3) Later in this course, we will learn that the function, arctan x, is equivalent to a power series for x on the interval -1sxs: 2n+1 (-1)" arctan x = We can use this power series to approximate the constant π . a) First, evaluate arctan1). (You do not need the series to evaluate it.) b) Use your answer from part (a) and the power series above to find a series representation for (The answer will be just a series-not...
k for 2 5. Consider the function f(x) = 37T 0 for 2 Hint: See examples of functions of a generic period t; James, 4th ed. pg. 581, Ex. 7.7 & 7.8 (a) State wether it has even or odd symmetry (b) Find the Fourier series representation for f. Plot graphs of the first three partial sums SI (c) Using the result in part (b), show that 1 + 1 +.. 7 4
k for 2 5. Consider the function...
1. Let f(1) = ***+3. (a) (3 points) Sketch the region S below the graph of y = f(x) and between x = 0 and * = 4. Remember to label axes and important points! (b) (4 points) Approximate the area A of the region S using rectangles by dividing (0,4into four equal subintervals and creating rectangles with the right endpoints. Here you will be calculating R4. It may help to draw the rectangles on your graph (c) (2 points)...
15. Let f(x) = 2 . 2+x a) Find the power series representation of f(x) centered at o b) Use the power series representation to find ½ dx. 16. Find the Taylor Series for f(x) = sin (2x) centered at T.
15. Let f(x) = 2 . 2+x a) Find the power series representation of f(x) centered at o b) Use the power series representation to find ½ dx. 16. Find the Taylor Series for f(x) = sin (2x) centered...
Question 4 10 pts #3. Consider the function f(x) = 2 3 (a) (5pts) Find a power series for f(x) centered at 0. (b) (5pts) Determine the interval of convergence of f(x). Upload Choose a File Question 5 10 pts #4. (a) (5pts) Find the Taylor series for f(x) = cos x, centered at 0. (Note: You can refer to the textbook.) (b) (5pts) Using (a), find the Maclaurin series for g(x) = cos(a). Write the first five terms of...
Consider the graph 12 10 6, 9) y-f(x 8 (2, 7) (4, 5) (0, 3) (8, 0) 10 (a) Using the indicated subintervals, approximate the shaded area by using lower sums s (rectangles that lie below the graph of f) (b) Using the indicated subintervals, approximate the shaded area by using upper sums S (rectangles that extend above the graph of f) +-14 points SullivanCalc1 5.1.019 Approximate the area A under the graph of function f from a to b...
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