# 16032022 신홍석

## 1585 days 전, tlsghdtjr456 작성

var('x') f(x)=-1/2*x^2 v(x)=-2*x+2 p1=plot(f(x),(x,1,3)) p2=plot(v(x),(x,1,3),color='red') p1+p2
limit((x^1000-1)/(x-1), x=1)
 1000 1000
var('x') f(x)=sin(sin(x)) x0=pi;y0=0 df(x)=diff(f(x), x) print df(x) m=df(x0) p1=plot(f(x), (x, 0, 2*pi)) p2=plot(y0+m*(x-x0), (x, 0, 2*pi), color='red') show(p1+p2)
 cos(x)*cos(sin(x))  cos(x)*cos(sin(x)) 
var('x') f(x)=sqrt(1+4*sin(x)) x0=0;y0=1 df(x)=diff(f(x), x) print df(x) m=df(x0) v(x)=m*(x-x0)+y0 print v(x) g(x)=-(1/m)*(x-x0)+y0 print g(x)
 2*cos(x)/sqrt(4*sin(x) + 1) 2*x + 1 -1/2*x + 1 2*cos(x)/sqrt(4*sin(x) + 1) 2*x + 1 -1/2*x + 1
var('x, y') f(x, y)=9*x^2+y^2-9 dx=diff(f(x,y),x) dy=diff(f(x,y),y) v(x,y)=dy/dx ddx=diff(v(x,y),x) ddy=diff(v(x,y),y) print ddy/ddx
 -x/y -x/y
var('x, y') f(x, y)=x^2+x*y+y^2 fx=diff(f(x, y), x) fy=diff(f(x, y), y) m(x,y)=-fx/fy x0=1 y0=1 v(x)=(-x+2) p1=implicit_plot(f(x, y)==3, (x, -2, 2), (y, -2, 2)) p2=implicit_plot(y-y0==m(x0,y0)*(x-x0), (x, -2, 2),(y, -2, 2), color='red') show (p1+p2) g(x)=m(x0,y0)*(x-x0)+y0 print g(x)
  -x + 2  -x + 2