Use algebra to evaluate the limit lim h->0((2−h)^2−8)/h
just expand the expression ...
((2−h)^2−8)/h
= (4 - 4h + h^2 - 8)/h
I sense something is wrong here, are you sure it wasn't
lim ((2-h)^3 - 8)/h ????
then it would make sense.
I'm sorry, yeah it's ((2-h)^3 - 8)/h
ok, expand that ...
((2−h)^3−8)/h
=( 8 - 12h + 6h^2 - h^3 - 8)/h
= (-12 + 6h - h^2)
so lim (-12 + 6h - h^2) as h ---> 0
= -12
Oh ok... thanks a lot, I was typing 12 all this time....
To evaluate the limit lim h->0 ((2−h)^2−8)/h, we can apply algebraic techniques.
Step 1: Expand the numerator:
((2−h)^2−8) = (4 - 4h + h^2 - 8) = (h^2 - 4h - 4)
Step 2: Rewrite the expression:
lim h->0 ((h^2 - 4h - 4)/h)
Step 3: Factor out an h from the numerator:
lim h->0 (h(h - 4) - 4)/h
Step 4: Cancel out the common factor of h in the numerator and denominator:
lim h->0 (h - 4) - 4
Step 5: Evaluate the limit:
As h approaches 0, (h - 4) will also approach 0. Therefore, the limit is equal to -4.
Therefore, lim h->0 ((2−h)^2−8)/h = -4.