Calculus UNIT203 Definition of the Derivative!

2813 days ago by MATH4R2013

#1a) what's the slope of the tangent line at t=1sec? [h]=ft of ball off the ground h(t)=1024-16*t^2 show(h(t)) show((h(1)-h(8))/(1-8)) show((h(1)-h(7))/(1-7)) show((h(1)-h(6))/(1-6)) show((h(1)-h(5))/(1-5)) show((h(1)-h(4))/(1-4)) show((h(1)-h(3))/(1-3)) show((h(1)-h(2))/(1-3)) plot(h(t),0,8) 
       








#1b) apply definition of f'(x) to f(x)=1024-16*x^2 f(x)=1024-16*x^2 var('h') show(f(x+h)) show(expand(f(x+h)-f(x))) show(((expand(f(x+h)-f(x)))/h).simplify_rational()) show(lim((f(x+h)-f(x))/h,h=0)) 
       



#2) apply definition of f'(x) to f(x)=x^2 f(x)=x^2 var('h') show(expand(f(x+h))) show(expand(f(x+h)-f(x))) show(((expand(f(x+h)-f(x)))/h).simplify_rational()) show(lim((f(x+h)-f(x))/h,h=0)) 
       



#3) apply definition of f'(x) to f(x)=x^3 f(x)=x^3 var('h') show(expand(f(x+h))) show(expand(f(x+h)-f(x))) show(((expand(f(x+h)-f(x)))/h).simplify_rational()) show(lim((f(x+h)-f(x))/h,h=0)) 
       



#4) apply definition of f'(x) to f(x)=x^4 f(x)=x^4 var('h') show(expand(f(x+h))) show(expand(f(x+h)-f(x))) show(((expand(f(x+h)-f(x)))/h).simplify_rational()) show(lim((f(x+h)-f(x))/h,h=0)) 
       



#5) apply definition of f'(x) to f(x)=x^5 f(x)=x^5 var('h') show(expand(f(x+h))) show(expand(f(x+h)-f(x))) show(((expand(f(x+h)-f(x)))/h).simplify_rational()) show(lim((f(x+h)-f(x))/h,h=0))