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Here are several interesting graphs plotted with Advanced Grapher. Regression The equations of curves are obtained with the help of the regression analysis of the tabular data (which are shown by points) Y(x)=-(1.1100319*10^(-8))*x^9 + (4.2010685*10^(-8))*x^8 + (4.8204417*10^(-6))*x^7 - (1.9123759*10^(-5))*x^6 - (6.0569249*10^(-4))*x^5 +0.0026407*x^4+ 0.0193816*x^3 - 0.0956714*x^2 + 1.6439131*x + 1.0095675 (polynomial regression, polynomial power is 9) Y(x)=1.665949*x+1.3004023 (linear regression) Cassini curve R(a)=2^2*cos(2*a)+sqrt(2.5^4-2^4*sin(2*a)^2) Addition of oscillations Y(x)=sin(x+1)*3 Y(x)=sin(x+2)*2 Y(x)=sin(x+1)*3+sin(x+2)*2 Smoothing Table: 7 items Damped oscillations Y(x)=exp(-x/4)*10*cos(x*3) Y(x)=exp(-x/4)*10 Y(x)=-exp(-x/4)*10 Ellipse 3*x*x-2*x*y+x*4+y*8+3*y*y-8<0 3*x*x-2*x*y+x*4+y*8+3*y*y-8=0 Epicycloid X(t)=(6+2)*cos(t)-2*cos((6+2)/2*t);   Y(t)=(6+2)*sin(t)-2*sin((6+2)/2*t) R(a)=6 Equation and inequality x*sin(x)+y*sin(y)<0 x*sin(x)+y*sin(y)=0 Four-leaved rose R(a)=7*sin(2*a) Ortogonal oscillations X(t)=sin(2*t); Y(t)=sin(3*t) Resonance Y(x)=15/sqrt(4+(1.5*x-12/x)^2) Y(x)=15/sqrt(18+(1.5*x-12/x)^2) Slope fields dy/dx=1/x^2 dy/dx=x Y(x)=-1/x Y(x)=x*x/2-10 Tangents The equations of the tangents are obtained with the help of this program R(a)=5 X(y)=5 Y(x)=-0.5913984*x+5.8089414 Y(x)=0.5773502*x+5.7735026 X(y)=-5 Y(x)=-0.5773504*x-5.773503 Y(x)=0.5773504*x-5.773503 Integer part Y(x)=int(x)