Key to MATLAB Exercise 7 School of Mathematical Sciences Xiamen Univer http:/edjpkc.xmu.ed > clear; syms x; y5=(tan(x)(tan(x))) > limit(y5, x, pi/4, right) ans > clear; syms x; y=tan(x/2) >>limit(y, x, pi, left") 5.1) > clear; syms x n h, y=((x+h)n-x'n >>Limit(y, h,0) > simplify(z)) ans x^(-1+n)°n >>clear; syms xn, yxn, ans > simplify(difi(y, x)) x^(-1+n)°n >ssd)88(x3502x2+7) > clear; syms x g:g=(x3-5)(2x2+7) > compose(diff(g x),0) ans > clear; syms x y g:g=(x3 y-5*y)(2*x2+7) 3*x^2(2*x^2+7)4*(X^~3-5)/(2*x~2+7)^2*x > subs(g xy, 1) ans 0.5309 Ex7-3Key to MATLAB Exercise 7  School of Mathematical Sciences Xiamen University  http://gdjpkc.xmu.edu.cn  Key to Ex7­3  5) >> clear; syms x; y5=(tan(x)^(tan(x)));  >> limit(y5,x,pi/4,’right’) ans =  1  6) >> clear; syms x; y=tan(x/2);  >> limit(y,x,pi,'left')  ans =  Inf 5.  1) >> clear; syms x n h; y=((x+h)^n­x^n)/h;  >> z=limit(y,h,0) z =  x^n/x*n  >> simplify(z)) ans =  x^(­1+n)*n  2) >> clear; syms x n ; y= x^n;  >> diff(y, x) ans =  x^n/x*n  >> simplify(diff(y,x)) ans =  x^(­1+n)*n  6.  1) >> clear; syms x g; g=(x^3­5)/(2*x^2+7);  >> subs(diff(g,x),0) Or >> clear; syms x g; g=(x^3­5)/(2*x^2+7);  >> compose(diff(g,x),0) ans =  0  2) >> clear; syms x y g; g=(x^3*y­5*y)/(2*x^2+7);  >> g_xy=diff(diff(g,x),y) g_xy =  3*x^2/(2*x^2+7)­4*(x^3­5)/(2*x^2+7)^2*x  >> subs(g_xy, 1) ans =  0.5309  Or