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1. | a>0, c>0, b>0, d<>0 y=ae-cxsin(bx+d) 0≤x<∞ | b>a>0 x=(b-a)*cos(j)+a*cos((b-a)*j/a) y=(b-a)*sin(j)-a*sin((b-a)*j/a) (b/a) 0≤j≤2p | a>0 r=2a2*cos2 (2j), -3p/4≤j≤5p/4 |
2. | y=sh(x)=(ex-e-x)/2 -∞<x<∞ | , a>0, 0≤j≤2p x=a*cos(j)*(1+cos(j)) y=a*sin(j)*(1+cos(j)) | a>0, 0≤j≤2p r=2a*cos(j) |
3. | a>0, -∞<x<∞ y=cos(x)/a | -∞<j<∞ x=a*(j2-1)/ (j2+1) y=a*j*(j2-1)/ (j2+1) | 0<c<a<cÖ2, 0≤j≤2p, r2=c2*cos(2j)Ö(c4*cos2(2j)+(a4-c4)) |
4. | y=xb/a (b/a)>0, a, b , , a-, 0≤x<∞ | a>0, 0≤j≤2p y=a*cos3(j) x=a*sin3(j) | a>0, -p/2<j<p/2 r=a(4cos(5*j)-1/cos(5*j)) |
5. | b<0, c<0, -∞<x<∞ y=a+b/x+c/x2 | b>a>0, l>1, 0<j<2π, (b/a) x=(b-a)sin(j)-l*a*sin((b-a)*j/a) y=(b-a)cos(j)+l*a*cos((b-a)*j/a) | -p/2<j<p/2 r=a*sin2(j)/cos(j) |
6. | a>0, c=0, b>0, d<>0 y=ae-cxsin(bx+d) 0≤x<∞ | 0≤j<∞ x=(j/2)*cos(j) y=(j/2)*sin(j) | , 0<a<b<2a 0≤j≤2p r=a*cos(j)+b |
7. | y=th(x)=(ex-e-x)/ (ex+e-x) -∞<x<∞ | a>0, b>0, l>1, 0≤j≤2π, (b/a) x=(a+b)cos(j)-l*a*cos((a+b)*j/a) y=(a+b)sin(j)-l*a*sin((a+b)*j/a) | 0<j<π r=-a*cos (2j)/ sin (j) |
8. | abc≠0, a>0,c>0, b<0, y=axbecx 0≤x<∞ | , a>0, -∞<j<∞ x=a(j-sin(j)) y=a(1-cos(j)) | a>0 r=2a2*cos2 (2j), -p/4≤j≤p/4, 3p/4≤j≤5p/4 |
9. | , -∞<x<∞ y=ch(x)=(ex+e-x)/2 | a>0, b≥2a, 0≤j≤2p x=a*cos2(j)+b*cos(j) y=a*cos(j)sin(j)+b*sin(j) | a>0, b>=2 r=2a2*cos2 (b*j), -p/4≤j≤p/4, 3p/4≤j≤5p/4 |
10. | a>0, -∞<x<∞ y=cos(x/a) | b>a>0 x=(b-a)*cos(j)+a*cos((b-a)*j/a) y=(b-a)*sin(j)-a*sin((b-a)*j/a) (b/a)= p/q, p,q , 0≤j≤2qp | c>0, a>cÖ2, 0≤j≤2p, r2=c2*cos(2j)Ö(c4*cos2(2j)+(a4-c4)) |
11. | y=xb/a (b/a)<0, a, b , , a-, 0≤x<∞ | -∞<j<∞ x=3*a*j/(1+j3) y=3*a*j2/(1+j3) | , a>0, 0≤j≤2p r=a*(1+cos(j)) |
12. | a>0, -∞<x<∞ y=cos(x*a) | a>0, 0≤j≤2p x=a*cos3(j) y=a*sin3(j) | , 0<b<a, 0≤j≤2p r=a*cos(j)+b |
13. | y=th(x)=(ex+e-x)/ (ex-e-x) -∞<x<∞ | , a>0, b>0 x=(a+b)*cos(j)-a*cos((a+b)*j/a) y=(a+b)*sin(j)-a*sin((a+b)*j/a) (b/a) 0≤j≤2p | a>0 r=2a2*sin2 (2j), 0≤j≤p/2, p≤j≤3p/2 |
14. | abcd≠0, 0<a<1, c>0, b>0, d>0, -∞<x<∞ y=aebx+cedx | 0<a<b<2a, 0≤j≤2p y=acos2(j)+bcos(j) x=acos(j)sin(j)+bsin(j) | a>0, 0≤j≤2p r=2a/cos(2j) |
15. | abc≠0, a>0,c>0, 0<b<1, y=axbecx 0≤x<∞ | , a>0 -∞<j<∞ y=a(j-sin(j)) x=a(1-cos(j)) | c>0, a=c, 0≤j≤2p, r2=c2*cos(2j)Ö(c4 cos2(2j)+(a4-c4)) |
16. | abcd≠0, a>0,c<0, b>0, d>0, -∞<x<∞ y=aebx+cedx | -∞<j<∞ x=a*j2/(1+j2) y=a*j3/(1+j2) | a>0 r=a/j 0<j<∞ |
17. | a>0, b>0, y=b*exp(-(ax)2) -∞<x<∞ | a>0, b>0, 0<l<1, 0≤j≤2π, (b/a) x=(a+b)cos(j)-l*a*cos((a+b)*j/a) y=(a+b)sin(j)-l*a*sin((a+b)*j/a) | a>0 r=2a2*sin2 (2j), -p≤j≤p |
18. | abcd≠0, a<0,c>0, b<0, d>0, -∞<x<∞ y=aebx+cedx | , b>0, -∞<j<∞, a>0 a<0 ( ), x=a*ch(j)=a*(ej+e-j)/2 y=b*sh(j)=b*(ej-e-j)/2 | , a>0, 0≤j≤2p r=a*(1+sin(j)) |
19. | abc≠0, a>0,c<0, b>1, y=axbecx 0≤x<∞ | 0<b<a, 0≤j≤2p x=acos2(j)+bcos(j) y=acos(j)sin(j)+bsin(j) | , a>0, -π/2<j<π/2 r=-a*cos (2j)/ cos (j) |
20. | b>0, c>0, a>0, -∞<x<∞ y=a+b/x+c/x2 | , a>0, b>0 x=(a+b)*sin(j)-a*sin((a+b)*j/a) y=(a+b)*cos(j)-a*cos((a+b)*j/a) (b/a) 0≤j≤2p | a>0, 0≤j≤2p r=2a*sin(j) |
21. | abcd≠0, a>0,c>0, b>0, d<0, -∞<x<∞ y=aebx+cedx | b>a>0, l>1, 0≤j≤2π, (b/a) x=(b-a)cos(j)+l*a*cos((b-a)*j/a) y=(b-a)sin(j)-l*a*sin((b-a)*j/a) | 0<j<p r=a*cos2(j)/sin(j) |
22. | a=c√2, b=1/(c*√(2 π)), c>0, -∞<x<∞ y=b*exp(-(ax)2) | , a>0, 0<l<1, -∞<j<∞ x=a(j-l*sin(j)) y=a(1-l*cos(j)) | , a>0, b>=2a 0≤j≤2p r=a*cos(j)+b |
23. | ac≠0, a>0, 0<c<1, -1<b<1, -∞<x<∞ y=a*exp(bx+cx2) | a>0, l>1, 0≤j≤2p x=a(2cosj-lcos2j) y=a(2sinj-lsin2j) | , 0≤j≤∞, a>0 r=j/a |
24. | abc≠0, a>0,c<0, 0<b<1, y=axbecx 0≤x<∞ | b>a>0 y=(b-a)*cos(j)+a*cos((b-a)*j/a) x=(b-a)*sin(j)-a*sin((b-a)*j/a) (b/a)- 0≤j≤2p | , 0<b<a, 0≤j≤2p r=b- a*sin(j) |
a>0, a≠1, x>0 y=loga x | , a>0, 0≤j≤2p y=a*cos(j)*(1+cos(j)) x=a*sin(j)*(1+cos(j)) | a>0, 0≤j≤6p r=√(2*a*j) | |
b<0, c>0, a>0, -∞<x<∞ y=a+b/x+c/x2 | , a>0, b>0 y=(a+b)*cos(j)-a*cos((a+b)*j/a) x=(a+b)*sin(j)-a*sin((a+b)*j/a) (b/a)= p/q, p,q , 0≤j≤2qp | a>0, -π/2<j< π/2 r=a(4*cos(3j)-1/cos(3j)) | |
y=xb/a (b/a)<0, a, b , , a-, -∞<x<∞ | b>a>0 y=(b-a)*cos(j)+a*cos((b-a)*j/a) x=(b-a)*sin(j)-a*sin((b-a)*j/a) (b/a)= p/q, p,q , 0≤j≤2qp | (0<a<1), (a>1) r=b/(1+a*cos(j)), 0≤j≤2p, b>0 | |
Abc≠0, a>0,c<0, b<0, Y=axbecx 0≤x<∞ | , a>0, l>1, -∞<j<∞ x=a(j-l*sin(j)) y=a(1-l*cos(j)) | , 0<b<a, 0≤j≤2p r=a*sin(j)+b | |
y=eax, a≠0 -∞<x<∞ | a>0, l<>1, 0≤j≤2π x=a(1+l)cos(j) y=a(1-l)sin(j) | a>0, b>=2 r=2a2*sin2 (b*j), -p≤j≤p, | |
a>0, b>0, d<>0 y=a*sin(bx+d), -∞<x<∞ | a>0, b>0, l>1, 0≤j≤2π, (b/a) y=(a+b)cos(j)-l*a*cos((a+b)*j/a) x=(a+b)sin(j)-l*a*sin((a+b)*j/a) | a>0, b≥3, r=2a/cos(b*j) b-, 0≤j≤2p b-, 0≤j≤p | |
a>0, c<0, b>0, -∞<x<∞ y=1√(ax2+ba+c) ( ) | b>a>0, 0<l<1, (b/a)= p/q, p,q , 0≤j≤2qp, y=(b-a)cos(j)+l*a*cos((b-a)*j/a) x=(b-a)sin(j)-l*a*sin((b-a)*j/a) | a>0, 0≤j≤p r=a(4*cos(j)-1/cos(j)) | |
a>0, c>0, b>0, d<>0, x>=0 y=ae-cxsin(bx+d) | 0<a<b<2a, 0≤j≤2p x=acos2(j)+bcos(j) y=acos(j)sin(j)+bsin(j) | a>0, 0<j<2p r=2a/sin(2j) | |
a>0, c<0, b>0, -∞<x<∞ y=a+b/x+c/x2 | , a>0, 0≤j≤2p x=x0+a*cos(j) y=y0+a*sin(j) | a>0, b≥3, r=2a/sin(b*j) b-, 0<j≤2p b-, 0<j≤p | |
y=a3/(x2+a2) a>0, -∞<x<∞ | , a>0, b>0, 0≤j≤2π x=a*cos(j) y=b*sin(j) | -∞<j<∞, a>0, -1<b<1 r=a*ebj | |
y=xb/a (b/a)>0, a, b , , a-, -∞<x<∞ | , a>0, b>0, 0≤j≤2qp x=(a+b)*cos(j)-a*cos((a+b)*j/a) y=(a+b)*sin(j)-a*sin((a+b)*j/a) (b/a)= p/q, p,q , | r=b/(1+cos(j)), -p≤j≤p, b>0 | |
ac≠0, a>0, b>0, c<0, -∞<x<∞ y=a*exp(bx+cx2) | 0<a<b, -p/2<j<3p/2 x=a+b*cos(j) y=a*tg(j)-b*sin(j) | (0<a<1), (a>1) r=b/(1+a*sin(j)), 0≤j≤2p, b>0 |
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