204 Practice Finding f'(x) MrG 2013.0424

3108 days ago by MATH4R2012

#1) if f(x)=sin(x) find f'(x). f(x)=cos(x) g(x)=f(x).diff(x) show(g(x)) 
       
var('h') g(x)=(f(x+h)-f(x))/h show(g(x).simplify_trig()) show(limit(g(x),h=0)) 
       

show(limit(sin(h)/h,h=0)) show(limit((cos(h)-1)/h,h=0)) 
       

#2) if f(x)=1/x, then f'(x)=? f(x)=1/x g(x)=f(x).diff() show(f(x)) show(g(x)) 
       

var('h') g(x)=(f(x+h)-f(x))/h show(g(x).simplify_rational()) show(limit(g(x),h=0)) 
       

#3) if f(x)=sqrt(x), then f'(x)=? f(x)=sqrt(x) g(x)=f(x).diff() show(f(x)) show(g(x)) 
       

var('h') g(x)=(f(x+h)-f(x))/h show(g(x).simplify_trig()()) show(limit(g(x),h=0))