The first three Taylor polynomial approximations of f(x) = sin(x) are T(x) = x, - T(x)...

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The first three Taylor polynomial approximations of f(x) = sin(x) are T(x) = x, - T(x) = x 1/6x, T3(x) = x 1/6x3 + 1/120x5. Create a plot that superimposes the graphs of all four of these functions and that meets the following criteria: The functions should be plotted over the interval (2, 2). The function sin(x) should be plotted as a solid black curve with a line thickness of 3.5. The function T(x) should be plotted as a solid red curve with a line thickness of 2. The function T2(x) should be plotted as a dashed green curve with a line thickness of 2. The function T3(x) should be plotted as a dotted blue curve with a line thickness of 2. The label of the x-axis should be 'x' and have font size 25. The label of the y-axis should be y' and have font size 25. The title of the graph should be Graph of sin(x) and its Taylor Polynomials' and have font size 35. The domain of the plot should be (-2, 2). The range of the plot should be (-2,2). The font size for the tick labels along the x- and y-axes should be 20. A legend should be created. The font size for the legend should be 20. The legend should be located in the southwest corner of the plot. The grid and box should be turned on. The first three Taylor polynomial approximations of f(x) = sin(x) are T(x) = x, - T(x) = x 1/6x, T3(x) = x 1/6x3 + 1/120x5. Create a plot that superimposes the graphs of all four of these functions and that meets the following criteria: The functions should be plotted over the interval (2, 2). The function sin(x) should be plotted as a solid black curve with a line thickness of 3.5. The function T(x) should be plotted as a solid red curve with a line thickness of 2. The function T2(x) should be plotted as a dashed green curve with a line thickness of 2. The function T3(x) should be plotted as a dotted blue curve with a line thickness of 2. The label of the x-axis should be 'x' and have font size 25. The label of the y-axis should be y' and have font size 25. The title of the graph should be Graph of sin(x) and its Taylor Polynomials' and have font size 35. The domain of the plot should be (-2, 2). The range of the plot should be (-2,2). The font size for the tick labels along the x- and y-axes should be 20. A legend should be created. The font size for the legend should be 20. The legend should be located in the southwest corner of the plot. The grid and box should be turned on.