Solving a Math Problem with Constants and Limits: Find a and b

[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 don't know what to do

 

[Jameson]

Is this your problem?

\lim_{x\rightarrow{1}} \frac{a\sqrt{x+3}-b}{x-1}=1?

 

[Curious3141]

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 don't 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.