# M7solns3 - Solutions to Problems in Chapter Three Test Your...

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Solutions to Problems in Chapter Three Test Your Understanding Problems T3.1-1 The session is ± x = [5:20:85]; ± y = [10:30:130]; ± log(x.*y)-(log(x)+log(y)) ans = 1.0e-014 * -0.0444 0 -0.1776 -0.1776 0.1776 which are essentially zero, so the identity is correct. T3.1-2 The session is ± x = sqrt(2+6i) x= 2.0402 + 1.4705i ± abs(x) ans = 2.5149 ± angle(x) ans = 0.6245 ± real(x) ans = 2.0402 ± imag(x) ans = 1.4705 T3.1-3 The session is ± x = [0:0.4:2*pi]; ± exp(i*x)-(cos(x)+i*sin(x)) The answers are essentially zero, which demonstrates that the identity is correct. 3-1

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T3.1-4 The session is ± x = [0:0.4:2*pi]; ± asin(x)+acos(x)-pi/2 The answers are essentially zero, which demonstrates that the identity is correct. T3.1-5 The session is ± x = [0:0.4:2*pi]; ± tan(2*x)-2*tan(x)./(1-tan(x).^2) The answers are essentially zero, which demonstrates that the identity is correct. T3.1-6 The session is ± x = [0:0.1:5]; ± sin(i*x)-i*sinh(x) The answers are essentially zero, which demonstrates that the identity is correct. T3.2-1 The function Fle is function y = f5(x) y = exp(-0.2*x).*sin(x+2)-0.1; You can plot the function to obtain solution estimates to use with fzero , or you can simply try values of x between 0 and 10. The session is ± fzero( ± f5 ± ,0) ans = 1.0187 ± fzero( ± f5 ± ,4) ans = 4.5334 ± fzero( ± f5 ± ,6) ans = 7.0066 So the solutions are x =1 . 0187, 4.5334, and 7.0066. 3-2
T3.2-2 The function Fle is function y = f6(x) y = 1 + exp(-0.2*x).*sin(x+2); You can plot the function to obtain solution estimates to use with fminbnd , or you can simply try values of x between 0 and 10. The session is ± fminbnd( ± f6 ± ,0) ans = 2.5150 ± f6(ans) ans = 0.4070 ± fminbnd( ± f6 ± ,10) ans = 8.7982 ± f6(ans) ans = 0.8312 So the solutions are ( x, y )=(2 . 5150 , 0 . 4070) and ( x, y )=(8 . 7982 , 0 . 8312). T3.2-3 Refer to Example 3.2-2. Modify the function Fle given in the example to use an area of 200 ft 2 rather than 100 ft 2 . The function Fle is function L = channel(x) L = 200./x(1)-x(1)./tan(x(2))+2*x(1)./sin(x(2)); Because this problem is similar to Example 3.2-2, we can try the same guess as in the example. The session is ± x = fminsearch( ± channel ± ,[20,1]) x= 10.7457 1.0472 The answer is d =10 . 7457 ft and θ =1 . 0472 radians, or 60 .

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M7solns3 - Solutions to Problems in Chapter Three Test Your...

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