Question

Problem 1 MATLAB

A Taylor series is a series expansion of a function f()about a given point a. For one-dimensional real-valued functions, the general formula for a Taylor series is given as ia) (a) (z- a) (z- a)2 + £(a (r- a) + + -a + f(x)(a) (1) A special case of the Taylor series (known as the Maclaurin series) exists when a- 0. The Maclaurin series expansions for four commonly used functions in science and engineering are: sin(x) (-1)" - - V €R (2) (3) _£+...V(-1,1 (4) and tan (2) -1)" - . Va E [-1,1 (5) Create a figure that contains a subplot with two rows and two columns. For Eqtn. 2, Eqtn. 3, Eqtn. 4, and Eqtn. 5, plat the following five different plot lines: 1. The first term of the given series only 2. The first two terms of the given series 3. The first three terms of the given series 4. The first four terms of the given series 5. The exact function (i.e. what is listed on the far left-hand side of the equal sign) Each of the plot lines within a subplot should be a different color. Each plat should contain a legend, a title, and - and y-labels. Each plot should be created and edited using MATLAB lo not use the plat editor features in the MATLAB GUI to modify your plots). Create the plots within the 2 x 2 subplot, arranged as follows: commands (i.e. The plots for Eqtn. 2 should be in the top left subplot of the figure The plots for Eqtn. 3 should be in the top right subplot of the figure The plots for Eqtn. 4 should be in the bottom left subplot of the figure The plots for Eatn, 5 should be in the bottom right subplot of the figure Restrict each plot's domain (i.e. r values) to be from make your lowest value be -0.9. l incremented in steps of 0.1. Note that the domain for Eqtn. 4 does not include the point g 1. so for that plot -1to Hints: 1. Remember, just like in algebra every y-value should have a corresponding -value, and every x-value should have a corresponding y-value. If this is not true for your plotls), the legend colors may not work out as expected. 2. A sample figure is provided below

Answer 1

`Hey,

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y1=[];
y2=[];
y3=[];
y4=[];
y5=[];
x=-1:0.1:1;
y1=x;
y2=y1-x.^3/factorial(3);
y3=y2+x.^5/factorial(5);
y4=y3-x.^7/factorial(7);
y5=sin(x);
subplot(2,2,1);
plot(x,y1,x,y2,x,y3,x,y4,x,y5);
legend('First term','Second term','Third term','Fourth term','Exact functtion');
title('Plot of sin(x)');
y1=[];
y2=[];
y3=[];
y4=[];
y5=[];
x=-1:0.1:1;
y1=1;
y2=y1+x/factorial(1);
y3=y2+x.^2/factorial(2);
y4=y3+x.^3/factorial(3);
y5=exp(x);
subplot(2,2,2);
plot(x,y1,x,y2,x,y3,x,y4,x,y5);
legend('First term','Second term','Third term','Fourth term','Exact functtion');
title('Plot of e^x');
y1=[];
y2=[];
y3=[];
y4=[];
y5=[];
x=-0.9:0.1:1;
y1=x;
y2=y1-x.^2/(2);
y3=y2+x.^3/(3);
y4=y3-x.^4/(4);
y5=log(1+x);
subplot(2,2,3);
plot(x,y1,x,y2,x,y3,x,y4,x,y5);
legend('First term','Second term','Third term','Fourth term','Exact functtion');
title('Plot of ln(1+x)');
y1=[];
y2=[];
y3=[];
y4=[];
y5=[];
x=-1:0.1:1;
y1=x;
y2=y1-x.^3/(3);
y3=y2+x.^5/(5);
y4=y3-x.^7/(7);
y5=atan(x);
subplot(2,2,4);
plot(x,y1,x,y2,x,y3,x,y4,x,y5);
legend('First term','Second term','Third term','Fourth term','Exact functtion');
title('Plot of tan^-1(x)');

Figure 1 File Edit View Insert Iools Desktop Window Help EB Plot of e Plot of sin(x) First term First term 2,5 Second term Second term Third term Third term 0.5 Fourth term Fourth term 2 Exact functtion functtion 1.5 1 -0.5 0.5 0.6 -0.4 -0.2 0. 0.2 04 0.6 0 F 1 08 06 -04 -0.2 0 2 0.4 0.6 0.8 1 Plot of In(1+x) Plot of tan'1(x) First term First term 0.5 rm 0.5 Third torm 0 Fourth term Fourth term Exact functtion Exact functtion -0.5 0 1 -1.5 -0.5 2 2.5 0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -08 06 -0.4 -0.2 0 0 2 0 4 0.6 0.8 1 1:28 PM ENG O Type here to search 06/03/19

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