I was given this review problem in limits.(adsbygoogle = window.adsbygoogle || []).push({});

Lim_{X --> inf.}(1 - X + X^{2})^{1/2}- aX - b = 0.

I was asked to find a and b such that the above equation is satisfied, which I did as follows:

I removed an X from the entire thing and expanded the term in the brackets using binomial theorem. I get a = 1 and b = -1/2 which is the answer given in the text.

But here's what is bothering me. I did the sum another way and got a different answer and can't put my finger on the mistake.

I remove an X from the root term. And I split the limit across the functions since

Lim_{X-->Y}f(x) + g(x) = Lim_{X-->Y}f(x) + Lim_{X-->Y}g(x)

Lim_{X-->Y}f(x).g(x) = Lim_{X-->Y}f(x) . Lim_{X-->Y}g(x)

This gives me

Lim_{X --> inf.}X(1/X^{2}- 1/X + 1)^{1/2}- Lim_{X --> inf. (aX + b) = 0 = [LimX --> inf. X] [LimX --> inf.(1/X2 - 1/X + 1)1/2] - LimX --> inf. (aX + b) = 0 Now the term inside the root sign goes to 1. We are left with LimX --> inf. X - aX - b = 0 This way, the answer is a = 1 and b = 0. Why am I getting a different answer? I used all the limit rules correctly as far as I can see.}

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Something's wrong

**Physics Forums | Science Articles, Homework Help, Discussion**