State Function f and Number a...2

[nycmathguy]

Calculus
Section 2.7

Can you do 44 to end our Friday?

 

[MathLover1]

44.

lim((e^(-2+h)-e^(-2))/h,h->0).........................(e^(-2+h)-e^(-2))/h=(e^h - 1)/(e^2 h)=((1/e^2)((e^h - 1)/h)
=lim(((1/e^2)((e^h - 1)/h),h->0).......take constant out

=(1/e^2)*lim((e^h - 1)/h),h->0)................apply L’Hopital’s rule (e^h - 1)/h=e^h /1

=(1/e^2)*lim(e^h /1),h->0)......substitute h=0

=(1/e^2)*(e^0 /1)

=(1/e^2)*(1 /1)

=(1/e^2)

so,

 

[nycmathguy]

44.

lim((e^(-2+h)-e^(-2))/h,h->0).........................(e^(-2+h)-e^(-2))/h=(e^h - 1)/(e^2 h)=((1/e^2)((e^h - 1)/h)
=lim(((1/e^2)((e^h - 1)/h),h->0).......take constant out

=(1/e^2)*lim((e^h - 1)/h),h->0)................apply L’Hopital’s rule (e^h - 1)/h=e^h /1

=(1/e^2)*lim(e^h /1),h->0)......substitute h=0

=(1/e^2)*(e^0 /1)

=(1/e^2)*(1 /1)

=(1/e^2)

so, View attachment 3388

I think I'll try a few more this weekend and post my work, right or wrong.