Bài tập Giải tích 1 - Giải dạng 3: Matlab

DANG 3.1 

1.            syms x

                limit((9^x)/(factorial(n)),inf)

2.            syms x

                limit((1/(x+(-1)^x)),x,inf)

3.            syms x

                limit(sqrt(x^2+1)-(x^3+1)^(1/3),x,inf

4.            syms x

                limit((2^x+3^x)/(2^x-3^x),n,inf)

5.            syms x

                limit((2*x^3+3*x^2-9*log(x))/(3*(log(x))^7-x^3),x,inf)

6.            syms x

                syms m;syms m;limit((x^(1/m)-1)/(x^(1/n)-1),x,1)

7.            syms x

                limit((sqrt(x)+sqrt(x-1)-1)/sqrt(x^2-1),x,pi/4)

8.            syms x

                limit((sqrt(2)-2*cos(x))/(pi-4*x),x,pi/4)

9.            syms a x; 

                limit((tan(pi*x)/(2*a))*sin((x-a)/2),x,a)

docx 25 trang xuanthi 26/12/2022 3920
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  1. 13. syms x limit((2+x)^(1/x),x,0,'left') limit((2+x)^(1/x),x,0,'right') 14. syms x; Limit((abs(tan(4*x-pi))/(2*x-pi/2),x,pi/4,’right’) Limit((abs(tan(4*x-pi))/(2*x-pi/2),x,pi/4,’left ’) 15. syms x; limit((exp(1/x)+1/x)^x,x) 16. syms x limit((2^x-x^2)/(x-2),x,2) 17. syms x limit((tan(2*x)-3*asin(4*x))/(sin(5*x)-6*atan(7*x)),x,0) 18. syms x limit((exp(sin(x))+log(1-x)-1)/(asin(x)-sin(x)),x,0) 19. syms x limit((exp(x)+log(1-sin(x))-1)/((8-x^4)^(1/3)-2),x,0) 20. syms x limit(((1+x)^(1/x)-exp(1))/((sin(x))^2+x),x,0). 21. syms x limit((1+x*cos(x)-sqrt(1+2*x))/(log(1+x)-x),x,0) 22. syms x limit(1/cos(log(x))^(1/(cos(x) - 1)).??? 23. syms x limit(((2*x^2+3)/(2*x^2-1))^(x^2),x,0) 24. syms x limit((2-x/a)^(tan((pi*x)/(2*a))),x,a)
  2. y1=diff(y,t)/diff(x,t) y2=diff(y1,t)/diff(x,t) 12. syms x t; x=atan(t); y=log(1-t^2); y1=diff(y,t)/diff(x,t); y2=diff(y1,t)/diff(x,t) 13. syms x; subs(diff(exp(x)/(x^2),x,2),x,1) 14. syms x; subs(diff((x+sin(x))^x,x,1),x,pi/4) 15. syms x; subs(diff(log(x^2+sqrt(x^4+1)),x,1),x,0) 16. syms x; subs(diff((2*x+3)*exp(-x),x,1)) 17. syms x t; >> int(exp(-t^2)+t,0,x) ans = x^2/2 + (pi^(1/2)*erf(x))/2 >> diff(ans,x,1) ans = x + exp(-x^2)
  3. 11.KHONG HIEU KET QUA syms a x; int((1/(a^2+x^2)),x,0,inf) 12. syms x int(exp(-x^2),x,0,inf) 13. int(sin(x)/x,x,0,pi/2) 14.khong ra 15. int(x*exp(-x),x,inf,0) DANG 3.4 1. plot([1 2 -1 1],[1 3 2 1]) 2. syms x; x=linspace(-1,2,30); y=exp(x); x1=linspace(2,-1,30); y1=0*x1; plot([x x1],[y y1]) 3. syms x; x=linspace(0,2*pi,30); y=cos(x); x1=linspace(2*pi,0,30); y1=0*x1; plot([x x1],[y y1]) 4. syms t t=linspace(0,2*pi,30); x1=1+sin(t); y1=cos(t); x2=sin(t);
  4. 8. syms x; x=linspace(0,3,30); y=sinh(x); x1=linspace(3,0,30); y1=0*x1; plot([x x1],[y y1]) 9. syms t x=linspace(1,3,30); y=3./x; y1=4*ones(1,30)-x; plot(x,y); hold on plot(x,y1) 10. syms x t; x=linspace(0,1,30); y=asin(x); y1=pi/2+0*x; hold on plot(x,y); plot(x,y1); set(ezplot(0*t,t,[0 asin(1)])); DANG 3.5 1. syms x 2*int(abs(sin(x)),x,0,pi) 2. syms x int(abs(x^2-3*x),x,0,3) 3. syms x
  5. y=x^3/3 dt=2*pi*int(abs(y)*sqrt(1+(diff(y))^2),x,0,1) 2. syms x; f=x^2-x; a=solve(f); dt=double(2*pi*int(abs(f)*sqrt(1+(diff(f))^2),x,a(1,1),a(2,1))) 3. syms x; f=x; g=5*x+x^2; h=f-g a=solve(h) dientich=2*pi*double(int(abs(f-g)*sqrt(1+(diff(f-g))^2),x,a(1,1),a(2,1))) 4. syms x; y1=x^2/2; y2=sqrt(2*x); f=y1-y2 a=solve(f); dientich=abs(int(f,x,a(1,1),a(2,1))) 5. syms y; x=sqrt(4*(1-y^2/9)); a=solve(x) dientich=2*pi*double(int(abs(x)*sqrt(1+(diff(x,y))^2),y,a(2,1),a(1,1))) 6. syms x; y=sqrt(9*(1-x^2/4)); a=solve(y); dientich=2*pi*double(int(abs(y)*sqrt(1+(diff(y))^2),x,a(2,1),a(1,1))) 7. syms x; f=x^2-4;
  6. tt=abs(pi*int(f-g,x,0,a(2,1))) can than vi khi giai Phuong trinh ta dc 1 nghiem phuc nen loai ko tinh nghiem phuc do 8. 2*pi*int(abs(x*(((x^2+1))^2+5)),x,-2,2) DANG 3.8 1. syms x; f=x^(3/2) a=diff(f) l=double(int(sqrt(1-a^2),x,0,4)) 2. syms x; y=log(cos(x)); a=diff(y) b=sqrt(1-a^2); L=int(b,x,0,pi/4) 3. syms x; y=x^2; a=diff(y); b=sqrt(1-a^2); L=int(y,x,0,1) 4. 5. syms x; y=sqrt(2-x^2); L=int(y,x,0,sqrt(2)) %vi x^2=2-y^2,nen 0<=x<sqrt(2) DANG 3.9 1. dsolve('y-x*Dy=y*ln(x/y)','x') 2. dsolve('(1-x)*(Dy+y)=exp(-x)','y(2)=1','x') 3. dsolve('Dy-y*cotx=sinx','x')
  7. plot(x,x+1); hold on x1=linspace(1,4); plot(x1,3-x1.^2); plot(1,2,'*'); 2. syms x a limit(x-1,x,1,'left') subs(x-1,1) limit(a*x^2-2,x,1,'right') a=solve('a-2=0') x=linspace(-20,1); x1=linspace(1,30); plot(x,x-1);hold on plot(x1,2*x1.^2-2) plot(1,0,'*') 3. syms x a b; subs(a*x+1,pi/2) limit(a*x+1,x,pi/2,'left') limit(sin(x)+b,x,pi/2,'right') solve('(pi*a)/2+1=b+1') b=ans subs(b,1) x=linspace(-20,pi/2); x1=linspace(pi/2,20); plot(x,x+1); hold on plot(x1,sin(x1)+1.5708)
  8. limit(a*x^2+1,x,1,'left') a=solve('a+1=0') ezplot(1/(2^(1/(x-1))+1),[1,5]) hold on ezplot(a*x^2+1,[-6,1]); plot(1,0,'*'); 8. syms x a; subs(1/(2^(1/(x-1))+1),1) limit(1/(2^(1/(x-1))+1),x,1,'right') limit(a*x^2+1,x,1,'left') a=solve('a+1=0') ezplot(1/(2^(1/(x-1))+1),[1,5]) hold on ezplot(a*x^2+1,[-6,1]); plot(1,0,'*'); DANG 4.3 1. syms x limit((exp(x)-1)/x,x,0,'right') limit(x/2+1,x,0,'left') hold all ezplot((exp(x)-1)/x,[0,1]) ezplot(x/2+1,[-1,0]) ezplot(diff(x/2+1)*(x-0)+1,[-1,1]) %TIEP TUYEN 2. syms x limit(x,x,1,'left') limit(x^2-x,x,1,'right')
  9. DANG 4.6 KHONG HIEU RO?? 1. syms x f=(2*x-1)/(2*x^3+x^2-8*x+5) [t m]=numden(f) t= sym2poly(t) m=sym2poly(m) [m n p]= residue(t,m) solve((x-m(1))*(x-m(2))*(x-m(3))) 2. syms x F=(3*x^2-2)/(x^3+2*x^2-2*x+3) [t m]= numden(f) t= sym2poly(t) m=sym2poly(m) [m n p]= residue(t,m) solve(x-m(1)) m(2)*(x-n(3))+m(3)*(x-n(2)) simplify(ans) (x-n(2))*(x-n(3)) simplify(ans) 3. syms x f=(x^4-2)/(2*x^3+x^2-8*x+5) [t m]= numden(f) t=sym2poly(t) m=sym2poly(m) [m n p]= residue(t,m) solve((x-m(1))*(x-m(2))*(x-m(3)))
  10. DANG 4.8 1. syms x; >> f=exp(x)*sqrt(1-x) g=sqrt(1-x) a=solve(f-g) vox=pi*abs(int(f^2-g^2,x,a(1,1),a(2,1))) 2. syms x t hold all ezplot(x^2) ezplot(t,0+0*t) ezplot(2-x) 2*pi*int(abs(x*(x^2-2+x)),0,2) 3. syms x t hold all ezplot(2*x-x^2,0,3) ezplot(t,3+0*t,[0,3]) %hai do thi khong cat nhau nen khong tinh dc the tich 4. DANG 4.9 1. syms x real f=sqrt(1+x^2) ezplot(f,[0,1]) dien_tich= 2*pi*double(int(abs(f)*sqrt(1+diff(f)^2),0,1)) 2. syms x f=(sqrt(x)*(x-12))/6
  11. limit(f,x,-inf) limit(f,x,0,'right') limit(f,x,0,'left') a=limit(f/x,x,inf) b=limit(f-a*x,x,inf) ezplot(f,[-10,10]) hold on ezplot(a*x+b,[-10,10]) grid on 4. syms x; syms t; f=exp(1/x)-x limit(f,x,inf) limit(f,x,-inf) limit(f,x,0,'right') limit(f,x,0,'left') a=limit(f/x,x,inf) b=limit(f-a*x,x,inf) ezplot(f,[-10,10]) hold on ezplot(a*x+b,[-10,10]) grid on 5. syms x; syms t; f=x^2/sqrt(1+x^2) limit(f,x,inf) limit(f,x,-inf) limit(f,x,0,'right') limit(f,x,0,'left') a=limit(f/x,x,inf)
  12. y=1/2*x ezplot(y,[-10,50]) 2. syms x; f=exp(1/x) g=x^2+1 dhp=limit((f-subs(f,x,0))/x,x,0,'right') dht=limit((g-subs(f,x,0))/x,x,0,'left') tp=subs(dhp,x,0)*x+subs(f,x,0) tt=subs(dht,x,0)*x+subs(g,x,0) ezplot(f,[0,10]) hold on ezplot(g,[-10,0]) hold on ezplot(tp,[0,10]) hold on ezplot(tt,[-10,0]); y=0; hold on ezplot(0*x,[-50,50]) 3. f=(x-1)/log(x) g=(1-x)^2 limit((f-subs(g,1))/(x-1),x,1,'right') limit((g-subs(g,1))/(x-1),x,1,'left') ezplot(f,[1,10]) hold on ezplot(g,[-10,1]) plot(1,subs(g,1),'*')