302 MrG What's a Power Function?

2477 days ago by MATH4R2013

#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 
       
#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 
       
#2a) Y-axis symmetry f(x)=x^2 bool(f(-x)==f(x)) 
       
#2b) Origin symmetry f(x)=x^3 bool(f(-x)==-f(x)) 
       
#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)) 
       







#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 
       
#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 
       
#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) 
       





#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) 
       


#why won't this work? #show(solve(f(x)==100,x)) <-- commented as eval takes forever! 
       
#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)) 
       

show(l1[len(l1)-1].rhs().n()) 
       
l2=solve(q[a]*x^2==100,x) show(l2) show(l2[1]) show(l2[1].rhs()) show(l2[1].rhs().n(digits=100))