Algebraically Solving Limits

[fdragon]

Ok so how would you go about solving this equation algebraically.....

lim ((2+h)^2-4)/h
h-->0


I already know that the limit is 4 from looking at the graph but how would you solve it algebraically? :?

 

[soroban]

Hello, fdragon!

\(\displaystyle \:\lim_{h\to0}\frac{(2\,+\,h)\,-\,4}{4}\)

I already know that the limit is 4 from looking at the graph,
but how would you solve it algebraically?

As the risk of being offensively sarcastic, how about doing some algebra?
. . [By the way, it is not an equation . . . we don't 'solve' it.]

We have: \(\displaystyle \L\,\frac{(2\,+\,h)^2\,-\,4}{h}\;=\;\frac{4\,+\,4h\,+\,h^2 \,-\,4}{h} \;=\;\frac{4h\,+\,h^2}{h}\)

Factor and reduce: \(\displaystyle \L\,\frac{\not{h}(4\,+\,h)}{\not{h}}\)\(\displaystyle \;=\;4\,+\,h\)

Take the limit: \(\displaystyle \lim_{h\to0}(4\,+\,h) \;=\;4\)

 

[fdragon]

OMG thank you sooo much..... sorry my brain has been fried lately cause of school and not getting enought sleep.... I would've never got that ... I understand a little bit more now... I obviously need a tutor.