Plot y = exp(x) in the interval [-3, 3] using a solid line. Now plot a linear ap

Question

Plot y = exp(x) in the interval [-3, 3] using a solid line. Now plot a linear approximation of e^x (i.e. y = x) using a dashed line with a square marker in a different color and a quadratic approximation of e^x (i .e. y = 1 + x + x^2/2) using a dotted line and a circle marker in another color. Title the plot "Plots of Approximations of exp(x)." Label the y-axis as "Approximations of exp(x)" and the x-axis as "X". Use text to label the exp(x) curve at position (2, 8). Use gtext to label the linear and quadratic approximations of exp(x) appropriately. Set axes limits to [-3, 3, -5, 15]. b. Repeat the plots in a. but this time identify the plotted lines using legend instead of text and gtext.

Explanation / Answer

a.

x = -3:0.1:3;

y1 = exp(x);

y2 = x;

y3 = 1+x+(x.^2)/2;

plot(x,y1)

hold on

plot(x,y2, 'g-s')

hold on

plot(x,y3, 'c:o')

title('Plots of Approximations of e^{x}')

xlabel('x')

ylabel('Approximations of e^{x}')

text(2,8,' leftarrow e^{x}')

gtext('<-linear approximation of e^{x}')

gtext('<-quadratic approximation of e^{x}')

axis([-3 3 -5 15])

b.

x = -3:0.1:3;

y1 = exp(x);

y2 = x;

y3 = 1+x+(x.^2)/2;

plot(x,y1,x,y2, 'g-s',x,y3, 'c:o')

title('Plots of Approximations of e^{x}')

xlabel('x')

ylabel('Approximations of e^{x}')

legend('e^{x}','linear approximation of e^{x}','quadratic approximation of e^{x}')

axis([-3 3 -5 15])

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