2007 AB FRQs - AP Review

2772 days ago by MATH4R2013

#4a) f(t)=e^(-t)*sin(t) g(t)=diff(f(t),t) show(f(t)) show(factor(g(t))) show(solve(g(t)==0,t)) 
       


#4b) h(t)=diff(g(t),t) show(h(t)) var('A') equ=A*h(t)+g(t)+f(t)==0 show(equ) show(solve(equ,A)) 
       


#5a) tangent at t=5: y-y1=m*(x-x1) --> r-r(5)=r'(5)*(x-5) r(x)=2*(x-5)+30 show(r(x)) show(r(5.4)) 
       

#5b) v=(4/3)*pi*r^2 v=(4/3)*pi*r^3 show(v) show(diff(v,r)) show(4*pi*30^2*2) 
       


#5c) rsum show(2*4+3*2+2*1.2+4*.6+.5) 
       
#5d) rsum underestimates as function is decreasing 
       
#6a) var('k') f(x)=k*sqrt(x)-ln(x) g(x)=diff(f(x),x) h(x)=diff(g(x),x) show(f(x)) show(g(x)) show(h(x)) 
       


#6b) use second derivative test! show(g(1)) show(solve(g(1)==0,k)) 
       

#6c) show(solve(f(x)==0,k)) show(solve(h(x)==0,k)) show(solve(log(x)/sqrt(x)==4/sqrt(x),x))