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Constants

by gator
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gator
#1
Jan30-06, 07:57 PM
P: 16
Given a, b are constants and lim x approch 1, a root x+3 - b all over x-1 equals 1. Find a and b

No clue how to answer this, but this is what I think i can do

a) get rid of the sqrt
b) apply limit

See, the problem is I have to unknows so i dont know what to do
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Jameson
#2
Jan30-06, 08:15 PM
P: 788
Is this your problem?

[tex]\lim_{x\rightarrow{1}} \frac{a\sqrt{x+3}-b}{x-1}=1[/tex]?
Curious3141
#3
Jan30-06, 08:36 PM
HW Helper
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P: 2,943
Quote Quote by gator
Given a, b are constants and lim x approch 1, a root x+3 - b all over x-1 equals 1. Find a and b

No clue how to answer this, but this is what I think i can do

a) get rid of the sqrt
b) apply limit

See, the problem is I have to unknows so i dont know what to do
If the version posted in LaTex is correct, note that the denominator goes to zero when x->1. For the quotient to have a finite limit, the numerator must also go to zero when x is set to 1.

You get a simple linear relationship between a and b. ---(1)

Now you can use L'Hopital's Rule to evaluate a limit of the form 0/0. So differentiate both numerator and denominator. You know that the quotient of these two is also going to be 1 at the limit x->1.

So set x = 1 in that. The b term would have vanished, so you can now solve for a. Put that back in equation (1) and work out b, you're done.


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