Limits at Infinity with Radicals

[UTDCalcII]

Limits with radicals have always given me issues, and now my professor dropped a problem with no similar example in the book. If I can just get a little help getting started I'm sure I can get the rest.


Thanks in advance for any assistance!

 

[tkhunny]

You did not find a similar example in your book because you are not looking in the right book. Way back in Algebra 1, you learned how to find a common denominator and simplify complicated fractions. You will find an example, there.

Hint: Do numerator and denominator seprately, at first.

 

[lookagain]

Here is what I would do as an alternative:



I would multiply both the numerator of the larger fraction and the denominator

of the larger fraction by \(\displaystyle \dfrac{1}{\sqrt{t}} \) to get:



\(\displaystyle \displaystyle\lim_{t\to \infty}\dfrac{1 - \frac{1}{t}}{1 + \frac{1}{t}}\)


What does this equal?