- #1
Dissonance in E
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Homework Statement
find lim x---> infinity
sqrt(x + sqrt(x)) - sqrt(x)
Homework Equations
Conjugate multiplication.
The Attempt at a Solution
Ok so i know this is probably very easy yet it confuses me.
Im guessing youd need to multiply the numerator & denominator by the conjugate of the expression, and then work the expression into a form where all the x terms are denominators of a fraction so that as they approach inf, the fraction approaches 0.
(sqrt(x + sqrt(x)) - sqrt(x))(sqrt(x + sqrt(x)) + sqrt(x))
/ sqrt(x + sqrt(x)) + sqrt(x)
(x + sqrt(x) +sqrt(x)sqrt(x + sqrt(x)) -sqrt(x)sqrt(x + sqrt(x)) - x)
/ (sqrt(x + sqrt(x)) + sqrt(x))
sqrt(x)
/ (sqrt(x + sqrt(x)) + sqrt(x))
this is as far as i get, any help would be appreciated.
P.s: does this forum have a way of writing maths in a bit more easily comprehendable form?