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How do I solve this limit?
How do I solve this limit? I am having problems with the math! I can't seem to rationalize it and make the numbers work out! The hint tells me that I should rationalize the numerator and denominator.
Lim ( (7x-5)^1/2 - (7x+1)^1/2 ) / ( (28x+2)^1/2 - (28x+1) )^1/2
x--> infinity
So the limit as x approaches infinity
Like I said, I am having problems rationalizing it! Any suggestions for me?
1 Answer
- Alam Ko IyanLv 71 decade agoFavorite Answer
rationalizing factor of numerator: (7x-5)^1/2 + (7x+1)^1/2
rationalizing factor of denominator: (28x+2)^1/2 + (28x+1)^1/2
thus
lim [√(7x-5) - √(7x+1)] [√(7x-5) + √(7x+1)] [√(28x+2) + √(28x+1)] / [√(28x+2) - √(28x+1)] [√(28x+2) + √(28x+1)]
= lim [(7x-5) - (7x+1)] [√(28x+2) + √(28x+1)] / [(28x+2) - (28x+1)] [√(7x-5) + √(7x+1)]
= lim (-4)[√(28x+2) + √(28x+1)] / [√(7x-5) + √(7x+1)]
by now, only the biggest terms in the radicals matter .
= lim (-4) [2√28x] / [2√7x] .... simplify
= -8
