MORALES 3. (10 points) Use the second order Taylor polynomial of the sinc function to approximate the energy integral L.POa 17 (A) (B) 3 19 (C) 9 20 (D) 4 (E) 3
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please answer this multiple choice question The following statement concerns questions 1-3. The function f(t) is...
Not sure how to do this, please help! thank you! Consider the following function. f(x) =...
Not sure how to do this, please help! thank you!
Consider the following function. f(x) = x sin(x), a = 0, n = 4, -0.7 SXS 0.7 (a) Approximate f by a Taylor polynomial with degreen at the number a. T4(x) = T(x) when x lies in the given interval. (Round M up to the nearest integer. Round your answer to (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) four decimal places.) R4(x) (c) Check your...
Consider the following function. /(x)=x-5, a= 1, n= 2, 0.8SXS 1.2 (a) Approximate f by a Taylor p...
Consider the following function. /(x)=x-5, a= 1, n= 2, 0.8SXS 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a T2(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation x) ~ Tn(x) when x lies in the given interval. (Round your answer to six decimal places.) (c) Check your result in part (b) by graphing Rn(x) 0.6 0.4 0.2 0.6 0.4 0.2 0.9 0.9 1.2 -0.2 -0.4 -0.6 -0.2 -0.4 -0.6...
1. (Taylor Polynomial for cos(ax)) For f(x)cos(ar) do the following. (a) Find the Taylor polynomials T(x) about 0 for f...
1. (Taylor Polynomial for cos(ax)) For f(x)cos(ar) do the following. (a) Find the Taylor polynomials T(x) about 0 for f(x) for n 1,2,3,4,5 (b) Based on the pattern in part (a), if n is an even number what is the relation between Tn (x) and TR+1()? (c) You might want to approximate cos(az) for all in 0 xS /2 by a Taylor polynomial about 0. Use the Taylor polynomial of order 3 to approximate f(0.25) when a -2, i.e. f(x)...
a) Use MATLAB to find the Fourier Transform F(w) of the following function f(t). b) Plot...
a) Use MATLAB to find the Fourier Transform F(w) of the following function f(t). b) Plot F(w). Express the x-axis in [Hz]. Plot for f = -8Hz to 8Hz. f(t) = cos(27 (34))e-**" 0.8 0.6 0.4 0.2 f(t) appears to oscillate at 3 cycles/sec 0 -0.2 -0.4 -0.6 0.8 -1 2 -1.5 -0.5 0 0.5 1 1.5 2
1. (a) We want to develop a method for calculating the function sint dt f)-inf t...
1. (a) We want to develop a method for calculating the function sint dt f)-inf t 0 for small or moderately small values of x. This is a special function called the "sine integral", and it is related to another special function called the "exponential integral". It arises in diffraction problems. Derive a Taylor-series expression for f(x), and give an upper bound for the error when the series is terminated after the n-th order term. [HINT: (-1)"*z ? + R...
4: (1) The function erf(x)= $* e-rdt is called the error function. It is used in...
4: (1) The function erf(x)= $* e-rdt is called the error function. It is used in the field of probability and cannot be calculated exactly. However, one can expand the integrand as a Taylor polynomial and conduct integration. Find the approximate value of erf (2.0) using the first three terms of the Taylor series around t = 0. (2) Given f(3) = 6, f'(3) = 8, f "(3) =11, and all other higher order derivatives of f(x) are zero at...
hi i need help with the following & can you please put solutions in syntax form 1). f(t) satisfies the integral equa...
hi i need help with the following & can you please put solutions in syntax form 1). f(t) satisfies the integral equation: Find the solution of the integral equation using Fourier transforms. Your answer should be expressed as a function of t using the correct syntax. f(t) = 2). A signal f(t) has a Fourier transform given by Use Parseval's theorem to find the total energy content of the signal. Your answer can be expressed as a number accurate to...
Consider the following function. f[x) = x ln(3x), a = 1, n = 3, 0.8 lessthanorequalto...
Consider the following function. f[x) = x ln(3x), a = 1, n = 3, 0.8 lessthanorequalto x lessthanorequalto 1.2 Approximate f by a Taylor polynomial with degree n at the number a. T_3(x) = Use Taylor's Inequality to estimate the accuracy of the approximation f(x) = T_n(x) when x lies in the given Interval. (Round your answer to four decimal places.) |R_3 (x)| lessthanorequalto
1. This question concerns finding the roots of the scalar non-linear function f(x) = r2-1-sinx (1...
1. This question concerns finding the roots of the scalar non-linear function f(x) = r2-1-sinx (1 mark) (b) Apply two iterations of the bisection method to f(x) 0 to find the positive root. (3 marks) (c) Apply two iterations of the Newton-Raphson method to find the positive root. Choose (3 marks) (d) Use the Newton-Raphson method and Matlab to find the positive root to 15 significant (3 marks) (a) Use Matlab to obtain a graph of the function that shows...
question b please Consider the following function f(x) -x6/7, a-1, n-3, 0.7 sx 1.3 (a) Approximate f by a Taylor polynomial with degree n at the number a 343 (b) Use Taylor's Inequality to estimat...
question b please
Consider the following function f(x) -x6/7, a-1, n-3, 0.7 sx 1.3 (a) Approximate f by a Taylor polynomial with degree n at the number a 343 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ,(x) when x lies in the given interval. (Round your answer to eight decimal places.) IR3(x)0.00031049 (c) Check your result in part (b) by graphing Rn(x)l 2 1.3 0.00015 0 0.9 1.0 11 -0.00005 0.00010 -0.00010 0.00005 0.00015 0.8...
Not sure how to do this, please help! thank you!
Consider the following function. f(x) = x sin(x), a = 0, n = 4, -0.7 SXS 0.7 (a) Approximate f by a Taylor polynomial with degreen at the number a. T4(x) = T(x) when x lies in the given interval. (Round M up to the nearest integer. Round your answer to (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) four decimal places.) R4(x) (c) Check your...
Consider the following function. /(x)=x-5, a= 1, n= 2, 0.8SXS 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a T2(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation x) ~ Tn(x) when x lies in the given interval. (Round your answer to six decimal places.) (c) Check your result in part (b) by graphing Rn(x) 0.6 0.4 0.2 0.6 0.4 0.2 0.9 0.9 1.2 -0.2 -0.4 -0.6 -0.2 -0.4 -0.6...
1. (Taylor Polynomial for cos(ax)) For f(x)cos(ar) do the following. (a) Find the Taylor polynomials T(x) about 0 for f(x) for n 1,2,3,4,5 (b) Based on the pattern in part (a), if n is an even number what is the relation between Tn (x) and TR+1()? (c) You might want to approximate cos(az) for all in 0 xS /2 by a Taylor polynomial about 0. Use the Taylor polynomial of order 3 to approximate f(0.25) when a -2, i.e. f(x)...
a) Use MATLAB to find the Fourier Transform F(w) of the following function f(t). b) Plot F(w). Express the x-axis in [Hz]. Plot for f = -8Hz to 8Hz. f(t) = cos(27 (34))e-**" 0.8 0.6 0.4 0.2 f(t) appears to oscillate at 3 cycles/sec 0 -0.2 -0.4 -0.6 0.8 -1 2 -1.5 -0.5 0 0.5 1 1.5 2
1. (a) We want to develop a method for calculating the function sint dt f)-inf t 0 for small or moderately small values of x. This is a special function called the "sine integral", and it is related to another special function called the "exponential integral". It arises in diffraction problems. Derive a Taylor-series expression for f(x), and give an upper bound for the error when the series is terminated after the n-th order term. [HINT: (-1)"*z ? + R...
4: (1) The function erf(x)= $* e-rdt is called the error function. It is used in the field of probability and cannot be calculated exactly. However, one can expand the integrand as a Taylor polynomial and conduct integration. Find the approximate value of erf (2.0) using the first three terms of the Taylor series around t = 0. (2) Given f(3) = 6, f'(3) = 8, f "(3) =11, and all other higher order derivatives of f(x) are zero at...
Consider the following function. f[x) = x ln(3x), a = 1, n = 3, 0.8 lessthanorequalto x lessthanorequalto 1.2 Approximate f by a Taylor polynomial with degree n at the number a. T_3(x) = Use Taylor's Inequality to estimate the accuracy of the approximation f(x) = T_n(x) when x lies in the given Interval. (Round your answer to four decimal places.) |R_3 (x)| lessthanorequalto
1. This question concerns finding the roots of the scalar non-linear function f(x) = r2-1-sinx (1 mark) (b) Apply two iterations of the bisection method to f(x) 0 to find the positive root. (3 marks) (c) Apply two iterations of the Newton-Raphson method to find the positive root. Choose (3 marks) (d) Use the Newton-Raphson method and Matlab to find the positive root to 15 significant (3 marks) (a) Use Matlab to obtain a graph of the function that shows...
question b please
Consider the following function f(x) -x6/7, a-1, n-3, 0.7 sx 1.3 (a) Approximate f by a Taylor polynomial with degree n at the number a 343 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ,(x) when x lies in the given interval. (Round your answer to eight decimal places.) IR3(x)0.00031049 (c) Check your result in part (b) by graphing Rn(x)l 2 1.3 0.00015 0 0.9 1.0 11 -0.00005 0.00010 -0.00010 0.00005 0.00015 0.8...
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