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palm_ch3 - 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 diary diary1.txt x = [1:5];y = [0:2:8]; x.*y ans = 0 4 12 24 40 save session1 clear x y load session1 x.*y ans = 0 4 12 24 40 diary off type diary1.txt x = [1:5];y = [0:2:8]; x.*y ans = 0 4 12 24 40 save session1 clear x y load session1 x.*y ans = 0 4 12 24 40 diary off T3.3-1 The script file is % script file rad_deg.m rad_angle = [1:5]; deg_angle = rad_angle*(180/pi); angle_table = format bank disp( 0 radians degrees 0 ) disp(angle_table) The session is 3-1
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rad_deg radians degrees 1.00 57.30 2.00 114.59 3.00 171.89 4.00 229.18 5.00 286.48 T3.3-2 The script file is % script file sphere_v.m format bank r = [1:.1:2]; V = 4*pi*r.^3/3; vol_table = [r 0 ,V 0 ]; disp( 0 radius volume 0 ) disp(vol_table) The session is sphere_v radius volume 1.00 4.19 1.10 5.58 1.20 7.24 1.30 9.20 1.40 11.49 1.50 14.14 1.60 17.16 1.70 20.58 1.80 24.43 1.90 28.73 2.00 33.51 T3.3-3 The script file is % script file sphere a.m r = input( 0 Enter a value for the radius: 0 ); A = 4*pi*r.^2; disp( 0 The area of the sphere is: 0 ) A 3-2
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The session is sphere a Enter a value for the radius: 3 The area of the sphere is: A = 113.097 T3.4-1 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 T3.4-2 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 T3.4-3 The session is x = [0:.4:2*pi]; exp(i*x)-(cos(x)+i*sin(x)) The answers are essentially zero, which demonstrates that the identity is correct. 3-3
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T3.4-4 The session is x = [0:.4:2*pi]; asin(x)+acos(x)-pi/2 The answers are essentially zero, which demonstrates that the identity is correct. T3.4-5 The session is x = [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. T3.4-6 The session is x = [0:.1:5]; sin(i*x)-i*sinh(x) The answers are essentially zero, which demonstrates that the identity is correct. T3.5-1 The function file is function y = f5(x) y = exp(-.2*x).*sin(x+2)-.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( 0 f5 0 ,0) ans = 1.0187 fzero( 0 f5 0 ,4) ans = 4.5334 fzero( 0 f5 0 ,6) ans = 7.0066 So the solutions are x = 1 . 0187, 4.5334, and 7.0066. 3-4
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T3.5-2 The function file is function y = f6(x) y = 1 + exp(-.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( 0 f6 0 ,0) ans = 2.5150 f6(ans) ans = 0.4070 fminbnd( 0 f6 0 ,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). T3.5-3 Refer to Example 3.5-2. Modify the function file given in the example to use an area of 200 ft 2 rather than 100 ft 2 . The function file 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 3.5-1, we can try the same guess as in the example. The session is x = fminsearch( 0 channel 0 ,[20,1]) x = 10.7457 1.0472 The answer is d = 10 . 7457 ft and θ = 1 . 0472 radians, or 60 . T3.6-1 Using cell indexing to create a 1 × 4 cell array, the script file is: A { 1 } = [1:4]; A { 2 } = [0,9,2]; A { 3 } = [2:5]; 3-5
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A { 4 } = [6:8]; [x,y] = deal(A { 1:2 } ); B = [x,y] C = [A { 2 } ;A { 4 } ] [u,v] = deal(A { 2:3 } ); D = min([u,v]) T3.7-1 The script file is student(1).name = 0 John Smith 0 ; student(1).SSN = 0 392-77-1786 0 ; student(1).email = 0 [email protected] 0 ; student(1).tests = [67,75,84]; student(2).name = 0
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