The discussion revolves around evaluating the limit of the expression ((2+h)^4 - 16)/h as h approaches 0, which falls under the topic of limits in calculus.
Some participants have provided guidance on expanding and simplifying the expression, while others are exploring different approaches. There is a sense of progress as one participant indicates they have arrived at an answer, but no consensus on the method's ease has been established.
One participant mentions the answer in the textbook, which raises questions about the correctness of their methods and whether there is a simpler approach to the problem.
QuarkCharmer said:From:
[tex]\frac{(h^{2}+4h+8)(h^{2}+4h)}{h}[/tex]
You can distribute the numerator. It works the same way as if you were going to distribute/foil something like (a+b)(c+d)=(ac+da+bc+dc)
In this case it would be something more like this:
(a+b+c)(d+e+f) = (ad+ae+af+bd+be+bf+cd+ce+cf)
I think the easiest way of solving this problem (without using any calculus other than the limit) would be to expand the ()^4 right from the start. It's important to know how to distribute like shown above though.