# Solve limits by rationalizing

by famallama
Tags: limits, rationalizing, solve
 P: 9 1. The problem statement, all variables and given/known data Evaluate limit as x approaches 0 of (square root(4+x^4)-2)/x^4) algebraically by rationalizing the numerator. Show details 3. The attempt at a solution I rationalized the numerator and i see it as there is a root in the denominator now which is when i was taught to rationalize
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,552 Some time ago, we had a question on this forum basically asking why you always rationalize the numerator! The answer is, of course, that you don't always- although for many basic algebra problems, such as adding fractions, that helps. I have seen texts that devote quite a lot of time to rationalizing the numerator as well. Okay,if you have rationalized the numerator, you will have a square root in the denominator- but that doesn't hurt. It should be of the form $\sqrt{4+ x^4}+ 2$ which goes to 4, not 0, as x goes to 2. What happens to the rest of the fraction? That's the important thing!
 P: 9 that doesnt really help. I get x^4 -4(sqrt(4+x^4)) +6 on top of x^4(sqrt(4+x^))-2x^4
HW Helper
Thanks
P: 26,148
Solve limits by rationalizing

Hi famallama!

(have a square-root: √ )
 Quote by famallama that doesnt really help. I get x^4 -4(sqrt(4+x^4)) +6 on top of x^4(sqrt(4+x^))-2x^4
erm … the object is to have no √ on the top

Hint: your factors had a - on the top and the bottom … try it with a +
Math
Emeritus