#1a) Even Functions
p1=plot(x^2,-1,1,color='red')
p2=plot(x^4,-1,1,color='green')
p3=plot(x^6,-1,1,color='blue')
p1+p2+p3
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#1b) Odd Functions
p1=plot(x^3,-1,1,color='red')
p2=plot(x^5,-1,1,color='green')
p3=plot(x^7,-1,1,color='blue')
p1+p2+p3
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#2a) Y-axis symmetry
f(x)=x^2
bool(f(-x)==f(x))
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#2b) Origin symmetry
f(x)=x^3
bool(f(-x)==-f(x))
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#3) Limits
show(limit(x^2,x=+Infinity))
show(limit(x^2,x=-Infinity))
show(limit(x^4,x=+Infinity))
show(limit(x^4,x=-Infinity))
show(limit(x^3,x=+Infinity))
show(limit(x^3,x=-Infinity))
show(limit(x^5,x=+Infinity))
show(limit(x^5,x=-Infinity))
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#4) (p196 #1) f(x)=(x+1)^4
p1=plot(x^4,-2,2,color='red')
p2=plot((x+1)^4,-2,2,color='green')
p1+p2
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#5) (p196 #9) f(x)=(x-1)^5+2
p1=plot(x^5,-1,1,color='red')
p2=plot((x-1)^5,-1,1,color='green')
p3=plot((x-1)^5+2,-1,1,color='blue')
p1+p2+p3
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#6) (p196 #17) CBL estimate of g
#find and graph power regression y=f(x): [y]=height ball falls in feet vs. [x]=time of fall in seconds
var('a,b')
l=[[1.003,16],[1.365,30],[1.769,50],[2.093,70],[2.238,80]]
f(x)=a*x^b
q=find_fit(l,f,solution_dict=True)
show(q[a])
show(q[b])
show(f(a=q[a],b=q[b]))
show(points(l,color='blue')+plot(f(a=q[a],b=q[b]),(x,0,3),color='red')+plot(100,0,3,color='green'))
#f(x) should equal 0.5*g*x^2, estimate g in ft/sec/sec
f(x)=q[a]*x^q[b]
show(f(x))
show(q[a]*2)
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#how long does it take to hit the ground?
equ=f(x)==100
show(equ)
equ=equ/q[a]
show(equ)
equ=equ^(1/q[b])
show(equ)
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#why won't this work?
#show(solve(f(x)==100,x)) <-- commented as eval takes forever!
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#better to estimate (more decimals in q[b] means many more complex roots!)
l1=solve(q[a]*x^1.9==100,x)
show(l1)
show(len(l1))
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show(l1[len(l1)-1].rhs().n())
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l2=solve(q[a]*x^2==100,x)
show(l2)
show(l2[1])
show(l2[1].rhs())
show(l2[1].rhs().n(digits=100))
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