Homework Answers
ſAec r>c 2. (24 pts) Let f(x) = where A, B,CER, A, B +0. 10 <<C...
ſAec r>c 2. (24 pts) Let f(x) = where A, B,CER, A, B +0. 10 <<C (a) Show that f is differentiable at x = x=C. (b) Determine the first four terms of the Taylor series centered at r = C for f (2) using the definition of Taylor series. (c) If possible, find the Taylor series T (2) centered at 2 = C for f(c). (d) What's the radius and interval of convergence? (e) Find R.(C+). Can you find...
1,2,3, and 4 Here are some practice exercises for you. 1. Given f(x) e2, find the a. Maclaurin polynomial of degree 5 b. Taylor polynomial of degree 4 centered at 1 c. the Maclaurin series of f an...
1,2,3, and 4
Here are some practice exercises for you. 1. Given f(x) e2, find the a. Maclaurin polynomial of degree 5 b. Taylor polynomial of degree 4 centered at 1 c. the Maclaurin series of f and the interval of convergence d. the Taylor series generated by f at x1 2. Find the Taylor series of g(x) at x1. 3. Given x -t2, y t 1, -2 t1, a. sketch the curve. Indicate where t 0 and the orientation...
Question 2 6 pts Let T2(x) be the Taylor polynomial for f(x) = 2x + 2...
Question 2 6 pts Let T2(x) be the Taylor polynomial for f(x) = 2x + 2 centered at c = 1. Fill in the blanks in the paragraph below. Use exact values. The Error Notice that 4.2 = f(1.1) T2(1.1) = Bound says that the maximum possible value of the error is Tonal x-c"+1 1V 4.2 -T2(1.1) < (n + 1)! where K = and 2 - 1+1 (n+1)! Question 3 4 pts Fill in the blank. Use exact values...
Solve the Taylor Series. 1. (a) Use the root test to find the interval of convergence of-1)* に0 (b) Demonstrate that the above is the taylor series of f()- by writing a formula for f via taylor'...
Solve the Taylor Series.
1. (a) Use the root test to find the interval of convergence of-1)* に0 (b) Demonstrate that the above is the taylor series of f()- by writing a formula for f via taylor's theorem at α-0. That is write f(x)-P(z) + R(x) where P(r) is the nth order taylor polynomial centered at a point a and the remainder term R(x) = ((r - a)n+1 for some c between z and a where here a 0. Show...
1. find taylor series polynomials, p0 p1 p2 for f(x) at a=1 2. find taylor series...
1. find taylor series polynomials, p0 p1 p2 for f(x) at
a=1
2. find taylor series for f(x) centered at a=1
3. find the radius of convergence & interval of
convergence for the taylor series of f(x) centered at a=1
f(x) = 42
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...
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...
19. . 20 . 21 Find the Maclaurin series for f(x) using the definition of a...
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Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = e-3x f(x) = Σ n = 0 Find the associated radius of convergence R. R = Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) = 0.] f(x)...
For parts a, b, c and d, use the following function: f(x) = e-5x a) (3...
For parts a, b, c and d, use the following function: f(x) = e-5x a) (3 points) Write the Taylor polynomial of degree four for f(x) centered at 0. b) (2 points) Use the Taylor polynomial from part a to estimate the value of e-0.5. (Hint: let find x). c) (3 points) Write the series generated by f(x) at zero in sigma notation. d) (3 points) Find the radius of convergence and state the interval of convergence. d) (3 points)...
-1-1 arctan n n" n!5* (c) Find the interval of convergence and radius of convergence for )0301 i )e-3r) (d) Use the geometric series to write the power series expansion for i. f(1)- 2-4r, cen...
-1-1 arctan n n" n!5* (c) Find the interval of convergence and radius of convergence for )0301 i )e-3r) (d) Use the geometric series to write the power series expansion for i. f(1)- 2-4r, centered at a = 0. i.)4 centered at a-6. (e) Write the first 4 nonzero terms of the Maclaurin expansion for i, f(z) = z2 (e4-1) ii. /(x) = cos(3r)-2 sin(2x). (0) Use the Taylor Series definition to write the expansion for f(a)entered at (8) Use...
ſAec r>c 2. (24 pts) Let f(x) = where A, B,CER, A, B +0. 10 <<C (a) Show that f is differentiable at x = x=C. (b) Determine the first four terms of the Taylor series centered at r = C for f (2) using the definition of Taylor series. (c) If possible, find the Taylor series T (2) centered at 2 = C for f(c). (d) What's the radius and interval of convergence? (e) Find R.(C+). Can you find...
1,2,3, and 4
Here are some practice exercises for you. 1. Given f(x) e2, find the a. Maclaurin polynomial of degree 5 b. Taylor polynomial of degree 4 centered at 1 c. the Maclaurin series of f and the interval of convergence d. the Taylor series generated by f at x1 2. Find the Taylor series of g(x) at x1. 3. Given x -t2, y t 1, -2 t1, a. sketch the curve. Indicate where t 0 and the orientation...
Question 2 6 pts Let T2(x) be the Taylor polynomial for f(x) = 2x + 2 centered at c = 1. Fill in the blanks in the paragraph below. Use exact values. The Error Notice that 4.2 = f(1.1) T2(1.1) = Bound says that the maximum possible value of the error is Tonal x-c"+1 1V 4.2 -T2(1.1) < (n + 1)! where K = and 2 - 1+1 (n+1)! Question 3 4 pts Fill in the blank. Use exact values...
Solve the Taylor Series.
1. (a) Use the root test to find the interval of convergence of-1)* に0 (b) Demonstrate that the above is the taylor series of f()- by writing a formula for f via taylor's theorem at α-0. That is write f(x)-P(z) + R(x) where P(r) is the nth order taylor polynomial centered at a point a and the remainder term R(x) = ((r - a)n+1 for some c between z and a where here a 0. Show...
1. find taylor series polynomials, p0 p1 p2 for f(x) at
a=1
2. find taylor series for f(x) centered at a=1
3. find the radius of convergence & interval of
convergence for the taylor series of f(x) centered at a=1
f(x) = 42
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...
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...
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Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = e-3x f(x) = Σ n = 0 Find the associated radius of convergence R. R = Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) = 0.] f(x)...
For parts a, b, c and d, use the following function: f(x) = e-5x a) (3 points) Write the Taylor polynomial of degree four for f(x) centered at 0. b) (2 points) Use the Taylor polynomial from part a to estimate the value of e-0.5. (Hint: let find x). c) (3 points) Write the series generated by f(x) at zero in sigma notation. d) (3 points) Find the radius of convergence and state the interval of convergence. d) (3 points)...
-1-1 arctan n n" n!5* (c) Find the interval of convergence and radius of convergence for )0301 i )e-3r) (d) Use the geometric series to write the power series expansion for i. f(1)- 2-4r, centered at a = 0. i.)4 centered at a-6. (e) Write the first 4 nonzero terms of the Maclaurin expansion for i, f(z) = z2 (e4-1) ii. /(x) = cos(3r)-2 sin(2x). (0) Use the Taylor Series definition to write the expansion for f(a)entered at (8) Use...
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