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2. Produce the linear and quadratic Taylor polynomials for the following cases. Graph the function and these Taylor polynomials. (a) f(x)=√√x, a = 1 (c) f(x) = cos(x), a = 0 (b) f(x)=sin(x), a = π/4 (d) f(x) = log(1+e¹), a = 0

2. Produce the linear and quadratic Taylor polynomials for the following cases. Graph the function and these Taylor polynomials. (a) f(x)=√√x, a = 1 (c) f(x) = cos(x), a = 0 (b) f(x)=sin(x), a = π/4 (d) f(x) = log(1+e¹), a = 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please help answer #2 with out using matlab if possible, thank you.

 

 

The program uses the following program, named polyeval, to evaluate polynomials. The method used in the program is discussed in Section 1.3. function value = polyeval (x, alpha, coeff,n); % % function value = polyeval (x, alpha, coeff,n) % % Evaluate a Taylor polynomial at the points given in x, with % alpha the point of expansion of the Taylor polynomial, and % with n the degree of the polynomial. The coefficients are to % be given in coeff; and it is assumed there are n+1 entries in % coeff with coeff (1) the constant term in the polynomial value= coeff (n+1) *ones (size (x)); z = x-alpha; for in:-1:1 value= coeff (i) + z. *value; end 2. Produce the linear and quadratic Taylor polynomials for the following cases. Graph the function and these Taylor polynomials. (a) f(x)=√x, a = 1 (c) f(x) = cos(x), a = 0 (b) (d) f(x)=sin(x), a = π/4 f(x) = log(1+¹), a = 0
Transcribed Image Text:The program uses the following program, named polyeval, to evaluate polynomials. The method used in the program is discussed in Section 1.3. function value = polyeval (x, alpha, coeff,n); % % function value = polyeval (x, alpha, coeff,n) % % Evaluate a Taylor polynomial at the points given in x, with % alpha the point of expansion of the Taylor polynomial, and % with n the degree of the polynomial. The coefficients are to % be given in coeff; and it is assumed there are n+1 entries in % coeff with coeff (1) the constant term in the polynomial value= coeff (n+1) *ones (size (x)); z = x-alpha; for in:-1:1 value= coeff (i) + z. *value; end 2. Produce the linear and quadratic Taylor polynomials for the following cases. Graph the function and these Taylor polynomials. (a) f(x)=√x, a = 1 (c) f(x) = cos(x), a = 0 (b) (d) f(x)=sin(x), a = π/4 f(x) = log(1+¹), a = 0
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