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Finding the limit

  • Thread starter louie3006
  • Start date
  • #1
54
0

Homework Statement



find the limit if it exist :
lim (1/[x+Δχ] - 1/x) / Δχ
x->0-





The Attempt at a Solution


lim (1/[x+Δχ] - 1/x) / Δχ => lim -Δχ /(x+ Δx) / Δχ
x->0-
then what ? do i cancel the ΔX in the numerator with that in the denominator ? or whats the next step to solve this problem and did I do any mistake?
 

Answers and Replies

  • #2
Dick
Science Advisor
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That limit is undefined as x->0. Are you sure you don't mean delta X ->0? And, if so, sure, you want to cancel the thing that's going to 0. And don't write things like a/b/c without parentheses. It's not clear whether you mean (a/b)/c or a/(b/c). They are different.
 
  • #3
54
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oh yes, I'm sorry , I miss typed it its supposed to be delta x approaching 0 from the left hand side of the graph.
 
  • #4
Dick
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Ok. Let's write h instead of delta X, ok. You want limit h->0 (1/(x+h)-1/x)/h. I'm not really happy with -h/(x+h)/h for reasons beyond the parentheses.
 
  • #5
459
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You have 1/(x+dx) - 1/x

Cross multiply them, then see what you're left with.

edit: Oh you already did that, the dx cancels and as dx->0 it tends to -1/x^2 no?
 
  • #6
54
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it matches my answer but i wanted to make sure that i did the proper steps
 
  • #7
33,508
5,192
You have 1/(x+dx) - 1/x
Cross multiply them, then see what you're left with.
I think I understand what you meant to say, but cross multiplication applies when you have an equation with two rational expressions, such as
a/b = c/d

"Cross multiplication" results in ad = bc, and is equivalent to multiplying both sides of the equation by bd.
 
  • #8
459
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I think I understand what you meant to say, but cross multiplication applies when you have an equation with two rational expressions, such as
a/b = c/d

"Cross multiplication" results in ad = bc, and is equivalent to multiplying both sides of the equation by bd.
I mean

x/x(x+dx) - (x+dx)/x(x+dx) to get -dx/(x^2+dx)
 
  • #9
HallsofIvy
Science Advisor
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He meant, "get a common denominator and subtract the two fractions."
 

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