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Project: MTH161
Views: 1052

Create an animation showing the tangent line being approached from left.

@interact def _(n=slider(int(3),int(20),1,default=int(3),label='The number of the corners $=$')): n=int(n) p1=circle((0,0),1,color='black') corner=[[cos(2*i*pi/n),sin(2*i*pi/n)] for i in range(n)] p2=polygon2d(corner,fill=False) show(p1+p2,axes=False) %md Create an animation showing the tangent line being approached from right.

Create an animation showing the tangent line being approached from right.

x=var('x') u=var('u') w=var('w') Background=plot(x^2,0,4) Times=[1+1/t for t in range(20,1,-1)] for i in range(20): Times.append(2+2*i/20) Times=Times[::-1] Films=[plot(((w^2-1)/(w-1))*(u-1)+1,0,4,aspect_ratio=1/4,ymax=16,ymin=-1)+Background for w in Times] a=animate(Films) a.show()

Create an animation to show the tangent line of circle

Background=circle((0,0),1) Angles=[(pi/6+(pi/100)*n,(3*pi)/2-(pi*n)/60) for n in range(50)] Films=[Background+plot(((sin(Angles[n][0])-sin(Angles[n][1]))/(cos(Angles[n][0])-cos(Angles[n][1])))*(x-cos(Angles[n][0]))+sin(Angles[n][0]),-1.5,1.5,ymax=1.5,ymin=-1.5,aspect_ratio=1)+point([(cos(Angles[n][0]),sin(Angles[n][0])),(cos(Angles[n][1]),sin(Angles[n][1]))],rgbcolor='red',size=20) for n in range(50)] Films=Films+[Background+plot(-cot(2*pi/3)*(x-cos(2*pi/3))+sin(2*pi/3),-1.5,1.5,ymax=1.5,ymin=-1.5,aspect_ratio=1)+point((cos(2*pi/3),sin(2*pi/3)),rgbcolor='red',size=20)] a=animate(Films,aspect_ratio=1) a.show()

Showing the numerical data of the slopes mxm_x for xx approaching 11 from left.

Showing the numerical data of the slopes mxm_x for xx approaching 11 from right.

Compute the average speed over a period of time.

@interact def _(t=range_slider(0,20,default=(0,20),label='Find the average speed on the time interval$=$')): tt=var('tt') x= lambda tt: 4.9*tt^2 average_speed=n((x(t[0])-x(t[1]))/(t[0]-t[1]),digits=10) print('The average speed over the time interval ({},{}) is {}').format(t[0],t[1],average_speed)
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