Calculus UNIT205 Does continuity imply differentiability?

2814 days ago by MATH4R2013

#1) Does continuity imply differentiability? var('h') f(x)=abs(x) g(x)=lim((f(x+h)-f(x))/h,h=0) p1=plot(f(x),color='red') p2=plot(g(x),color='green') (p1+p2).show(aspect_ratio=1) 
       
#2) Does differentiability imply continuity? f(x)=(x+2)*(x-1)/(x-1) show(f(x)) p1=plot(f(x),-3,1,color='red') p2=plot(f(x),1,3,color='green') (p1+p2).show(aspect_ratio=1) 
       

#3) Find f'(x) given f(x)=abs(x) f(x)=abs(x) g(x)=diff(f(x),x) show(f(x)) show(g(x)) show(g(-2)) show(g(3)) 
       



#4) Find f'(x) given f(x)=sqrt(x^2) f(x)=sqrt(x^2) g(x)=diff(f(x),x) show(f(x)) show(g(x)) show(g(-2)) show(g(3))