Homework Answers
First,
write the equation of Taylor Series. According to the conditions
mentioned, derive the Taylor series expansion for order 3.
For the 2nd part of the question, by trial and error method, substitute two values, one smaller & the biggest value in the interval to find the value of n.
By inspection, you can write the expansion of higher order.
Add Answer to:
Problem 2 (35 points): Consider function f(x)-1/1) around zo 0 on the interval (0,0.5). (a) Find ...
Problem 1 (hand-calculation): Given f(x) - ze for z e [0,0.5], apply Taylor's theorem using zo...
Problem 1 (hand-calculation): Given f(x) - ze for z e [0,0.5], apply Taylor's theorem using zo 0 in the following exercises (a) Construct the Taylor polynomials of degree 4, p4(x) (b) Estimate the error associated with the polynomial in part (a) by computing an upper bound of the absolute value of the remainder.
The nth-order Taylor polynomial for a function f(x) using the h notation is given as: Pa...
The nth-order Taylor polynomial for a function f(x) using the h notation is given as: Pa (x + h) = f(x) + f'(a)h + salt) 12 + () +...+ m (s) n." The remainder of the above nth-order Taylor polynomial is defined as: R( +h) = f(n+1)(C) +1 " hn+1, where c is in between x and c+h (n+1)! A student is using 4 terms in the Taylor series of f(x) = 1/x to approximate f(0.7) around x = 1....
Question 1 (20 Points) Find the second Taylor polynomial P2(x) for the function f(x) = ex...
Question 1 (20 Points) Find the second Taylor polynomial P2(x) for the function f(x) = ex cos x about Xo = 0. Using 4-digit rounding arithmatic. (a). Use P2(0.7) to approximate f(0.7). (b). Find the actual error. (c). Find a bound for the error f(x) - P2(x) in using P2(x) to approximate f(x) on the interval [0, 1].
2. a) Find Ts(x), the third degree Taylor polynomial about x -0, for the function e2 b) Find a bound for the error in the interval [0, 1/2] 3. The following data is If all third order differences (not...
2. a) Find Ts(x), the third degree Taylor polynomial about x -0, for the function e2 b) Find a bound for the error in the interval [0, 1/2] 3. The following data is If all third order differences (not divided differences) are 2, determine the coefficient of x in P(x). prepared for a polynomial P of unknown degree P(x) 2 1 4 I need help with both. Thank you.
Quiz 5. Due Wednesday May 22, 2019. zo- e 1,e, 2-. Give the representation Consider interpolating the function In(x (without developing and 'simplifying in al) of the interpolation po...
Quiz 5. Due Wednesday May 22, 2019. zo- e 1,e, 2-. Give the representation Consider interpolating the function In(x (without developing and 'simplifying in al) of the interpolation polynomial Pa(z) expressed by Without calculating In(2) and P2(2) estimate the absolute error IIn(2) - P2(2)] s?
Quiz 5. Due Wednesday May 22, 2019. zo- e 1,e, 2-. Give the representation Consider interpolating the function In(x (without developing and 'simplifying in al) of the interpolation polynomial Pa(z) expressed by
Without calculating In(2)...
The Taylor polynomial approximation pn (r) for f(x) = sin(x) around x,-0 is given as follows: TL ...
The Taylor polynomial approximation pn (r) for f(x) = sin(x) around x,-0 is given as follows: TL 2k 1)! Write a MATLAB function taylor sin.m to approximate the sine function. The function should have the following header: function [p] = taylor-sin(x, n) where x is the input vector, scalar n indicates the order of the Taylor polynomials, and output vector p has the values of the polynomial. Remember to give the function a description and call format. in your script,...
- Question 2 3 points Consider the function f (x) = ln (1+2). (a) Enter the...
- Question 2 3 points Consider the function f (x) = ln (1+2). (a) Enter the degree-n term in the Taylor Series around x = 0. ((-1)^(n-1)*x^n)/n (b) Enter the error term En (2) which will also be a function of x and n. ((-1)^n*x^(n+1))/((n+1)*(1+z)^(n+1) (c) Find an upper bound for the absolute value of the error term when x > 0. It may help to remember that z is between x and 0. x^(n+1)/(n+1) 90 (d) Use this formula...
Consider the function f(x) 2x3 – 21x2 + 60x on the interval [-7, 6]. Find the...
Consider the function f(x) 2x3 – 21x2 + 60x on the interval [-7, 6]. Find the absolute extrema for the function on the given interval. Express your answer as an ordered pair (x, f(x)). Answer 2 Points Keypad Separate multiple entries with a comma. Absolute Maximum:// Absolute Minimum:
1. Consider the polynonial Pl (z) of degree 4 interpolating the function f(x) sin(x) on the interval n/4,4 at the e...
1. Consider the polynonial Pl (z) of degree 4 interpolating the function f(x) sin(x) on the interval n/4,4 at the equidistant points r--r/4, xi =-r/8, x2 = 0, 3 π/8, and x4 = π/4. Estimate the maximum of the interpolation absolute error for x E [-r/4, π/4 , ie, give an upper bound for this absolute error maxsin(x) P(x) s? Remark: you are not asked to give the interpolation polynomial P(r).
1. Consider the polynonial Pl (z) of degree 4...
please assist Problem 3 (8 points). Find a Taylor polynomial centered at 0 that approximates f(x)...
please assist
Problem 3 (8 points). Find a Taylor polynomial centered at 0 that approximates f(x) = et on the interval (-2,2] to within an error of 0.1.
Problem 1 (hand-calculation): Given f(x) - ze for z e [0,0.5], apply Taylor's theorem using zo 0 in the following exercises (a) Construct the Taylor polynomials of degree 4, p4(x) (b) Estimate the error associated with the polynomial in part (a) by computing an upper bound of the absolute value of the remainder.
The nth-order Taylor polynomial for a function f(x) using the h notation is given as: Pa (x + h) = f(x) + f'(a)h + salt) 12 + () +...+ m (s) n." The remainder of the above nth-order Taylor polynomial is defined as: R( +h) = f(n+1)(C) +1 " hn+1, where c is in between x and c+h (n+1)! A student is using 4 terms in the Taylor series of f(x) = 1/x to approximate f(0.7) around x = 1....
Question 1 (20 Points) Find the second Taylor polynomial P2(x) for the function f(x) = ex cos x about Xo = 0. Using 4-digit rounding arithmatic. (a). Use P2(0.7) to approximate f(0.7). (b). Find the actual error. (c). Find a bound for the error f(x) - P2(x) in using P2(x) to approximate f(x) on the interval [0, 1].
Quiz 5. Due Wednesday May 22, 2019. zo- e 1,e, 2-. Give the representation Consider interpolating the function In(x (without developing and 'simplifying in al) of the interpolation polynomial Pa(z) expressed by Without calculating In(2) and P2(2) estimate the absolute error IIn(2) - P2(2)] s?
Quiz 5. Due Wednesday May 22, 2019. zo- e 1,e, 2-. Give the representation Consider interpolating the function In(x (without developing and 'simplifying in al) of the interpolation polynomial Pa(z) expressed by
Without calculating In(2)...
The Taylor polynomial approximation pn (r) for f(x) = sin(x) around x,-0 is given as follows: TL 2k 1)! Write a MATLAB function taylor sin.m to approximate the sine function. The function should have the following header: function [p] = taylor-sin(x, n) where x is the input vector, scalar n indicates the order of the Taylor polynomials, and output vector p has the values of the polynomial. Remember to give the function a description and call format. in your script,...
- Question 2 3 points Consider the function f (x) = ln (1+2). (a) Enter the degree-n term in the Taylor Series around x = 0. ((-1)^(n-1)*x^n)/n (b) Enter the error term En (2) which will also be a function of x and n. ((-1)^n*x^(n+1))/((n+1)*(1+z)^(n+1) (c) Find an upper bound for the absolute value of the error term when x > 0. It may help to remember that z is between x and 0. x^(n+1)/(n+1) 90 (d) Use this formula...
Consider the function f(x) 2x3 – 21x2 + 60x on the interval [-7, 6]. Find the absolute extrema for the function on the given interval. Express your answer as an ordered pair (x, f(x)). Answer 2 Points Keypad Separate multiple entries with a comma. Absolute Maximum:// Absolute Minimum:
1. Consider the polynonial Pl (z) of degree 4 interpolating the function f(x) sin(x) on the interval n/4,4 at the equidistant points r--r/4, xi =-r/8, x2 = 0, 3 π/8, and x4 = π/4. Estimate the maximum of the interpolation absolute error for x E [-r/4, π/4 , ie, give an upper bound for this absolute error maxsin(x) P(x) s? Remark: you are not asked to give the interpolation polynomial P(r).
1. Consider the polynonial Pl (z) of degree 4...
please assist
Problem 3 (8 points). Find a Taylor polynomial centered at 0 that approximates f(x) = et on the interval (-2,2] to within an error of 0.1.
Most questions answered within 3 hours.
-
Critically discuss whether the Bretton Woods System has been
based on Keynesian principles. Please give me...
asked 3 seconds from now -
An ammeter with a scale ranging from 0 to 15mA has a resistance
of 5Omega. How...
asked 53 minutes ago -
def blur(img: Image) -> Image:
"""Blur Image, img, based on the given pixel_size
Hints:
- For...
asked 52 minutes ago -
a
carboxylic acid reacting with a strong base will form what
ion
asked 2 hours ago -
which value if any in each pair corresponds to a
faster reaction k=18.k=137
asked 2 hours ago -
Bus lines can be separated into two generic types, dedicated and
multiplexed.
i. What is the...
asked 4 hours ago -
This is 'Branding' course which is part of marketing.
1. As a brand manager of Nudie...
asked 4 hours ago -
You are considering the purchase of a new stock. The stock is
forecasted to pay a...
asked 4 hours ago -
vector a has componets Ax and Ay, and makes an angle theta with
the y-axis. Select...
asked 5 hours ago -
What were the problems of the american frontier after 1763 and how
did the British address...
asked 6 hours ago -
Why
isn’t pentanol (CH3 CH2 CH2 CH2 CH2 OH) very soluble in
water?
asked 6 hours ago -
In preparing its bank reconciliation for the month of April
2018, Haskins, Inc. has available the...
asked 8 hours ago