Just want to confirm the answer of a limit =)

Question

xapproachesinfinity · Answer

hope the limit is strange one lol

anonymous · Answer

$$ \lim_{h \rightarrow 0}\frac{ \frac{ 1 }{ (x+h)^2 } -\frac{ 1 }{ x^2 } }{ h }$$

anonymous · Answer

It's not a strange one, I'm just not confident in my answer and the solutions manual skips the even numbered questions qq

anonymous · Answer

My answer is $$\frac{- 1 }{ x }$$

jim_thompson5910 · Answer

your answer is unfortunately incorrect

anonymous · Answer

Well shoot

anonymous · Answer

Okay, I'll give it another go--TY.

jim_thompson5910 · Answer

hint: try to combine the fractions 1/(x+h)^2 - 1/(x^2)

xapproachesinfinity · Answer

yeah work on the denominator first like @jim_thompson5910 said

anonymous · Answer

Got a common denom., brought the h into it, cancelled and ended up with something like $$\lim_{h \rightarrow 0}\frac{ -2x-h }{ x^2(x+h)^2 }$$
so I'll work through the limit laws again

jim_thompson5910 · Answer

what happens when h goes to 0 for $\Large \frac{ -2x-h }{ x^2(x+h)^2 }$

anonymous · Answer

^ not supposed to plug in for this Q, wish I could though

jim_thompson5910 · Answer

you can now

anonymous · Answer

at least that tells me what I'm working towards

jim_thompson5910 · Answer

before you couldn't be cause you'd get a division by zero error

xapproachesinfinity · Answer

eh good going^_^

anonymous · Answer

they want us to go through limit laws tediously for practice - sol'n for a similar question doesn't plug in
thank you both thooughhh :)

jim_thompson5910 · Answer

the substitution property is a limit law

jim_thompson5910 · Answer

$$\Large \lim_{h\to 0}\left[\frac{ -2x-h }{ x^2(x+h)^2 }\right]$$

$$\Large \frac{ -2x-0 }{ x^2(x+0)^2 }$$

$$\Large \frac{ -2x }{ x^2(x)^2 }$$

$$\Large \frac{ -2x }{ x^4 }$$

$$\Large -\frac{ 2 }{ x^3 }$$

anonymous · Answer

haha thank youu

jim_thompson5910 · Answer

you're welcome

jim_thompson5910 · Answer

this confirms the answer http://www.wolframalpha.com/input/?i= \lim_{h%20\rightarrow%200}\frac{%20\frac{%201%20}{%20%28x%2Bh%29^2%20}%20-\frac{%201%20}{%20x^2%20}%20}{%20h%20}

jim_thompson5910 · Answer

you'll have to copy/paste the link

anonymous · Answer

Oooo, thanks again. I've never used Wolfram's calc before

jim_thompson5910 · Answer

it's very handy and you can even type LaTex formulas into it (and it will understand what to do with it)