Key to MATLAB Exercise 7 School of Mathematical Science http:/edjpkc.xmu.ed > clear; syms x uy; y=(x+log(sin(u)))(1/2) >>inverse(y, x) log(sin(u))+x > syms x yl y2; yl=sin(x), y2=asin(sin(x) >> x0=sym(pi/4): subs(y 1, xO) l/2*2^(1/2) ans 1/4 > syms x yl y2, yl=sin(x); y2=asin(sin(x)) > compose(yl, pi/4 ans 1/2*2^(1/2) > compose(y2, pi/4) l/4*p 4 > clear; syms n mx; yl=(tan(n*)-sin(m*x))/x Or > clear; syms n mx, yl=(tan(n*x)-sin(m*x))/x; n-m >> clear; syms x y, y2=(exp(x)-exp(y))/(x-y) >>limit(y2, x,y) ans exp(y) 3) > clear; syms x: y3=x3/(2*x+100) > limit(y3, x, +inf) ans > clear; syms x; y4=x 3/sin(x); ans NaN Ex7-2Key to MATLAB Exercise 7  School of Mathematical Sciences Xiamen University  http://gdjpkc.xmu.edu.cn  Key to Ex7­2  >> clear; syms x u y; y=(x+log(sin(u)))^(1/2);  >> finverse(y,x) ans =  ­log(sin(u))+x^2  3.  >> syms x y1 y2; y1=sin(x); y2=asin(sin(x));  >> x0=sym(pi/4); subs(y1,x0) ans =  1/2*2^(1/2)  >> subs(y2,x0) ans =  1/4*pi  Or >> syms x y1 y2; y1=sin(x); y2=asin(sin(x));  >> compose(y1,pi/4) ans =  1/2*2^(1/2)  >> compose(y2,pi/4) ans =  1/4*pi  4.  1) >> clear; syms n m x; y1=(tan(n*x)­sin(m*x))/x; >> limit(y1,0) Or >> clear; syms n m x; y1=(tan(n*x)­sin(m*x))/x; >> limit(y1) ans =  n­m  2) >> clear; syms x y; y2=(exp(x)­exp(y))/ (x­y);  >> limit(y2,x,y) ans =  exp(y) 3) >> clear; syms x; y3=x^3/(2*x+100);  >> limit(y3,x,+inf) ans =  Inf 4) >> clear; syms x; y4=x^3/sin(x);  >> limit(y4,x,­inf) ans =  NaN