Solution;
y=ex
P(x0,y0)=(0,1)
y′=ex
y′(0)=1
y′′=ex
y′′(0)=1
Radius of curvature;
R=y′′(x0)(1+y′(x0)2)23
By substitution ;
R=1(1+1)23=23=22
The curvature;
k=R1=221
The centre of curvature;
Let P be the center of curvature , given as (a,b)
a=xo−dx2d2ydxdy[1+(dxdy)2
a=0+exe2x=e0=1
b=yo+dx2d2y1+(dxdy)2
b=1+ex1+e2x=1+2=3
Therefore;
P=(1,3)
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