Please find lim x -> infinity (x - sqrtx)?

Question

^_^

Answer 1

infinity

Proof:

lim (x->infinity) {x-sqrtx} ==

lim (x->infinity) {(x^2-x)/(x+sqrtx)}

By L'hopital's Rule this ==

lim (x->infinity) {(2x-1)/(1+(1/(2sqrtx)))}

Since 2x-1 --> infinity and 1/(2sqrtx) --> 0,

this --> infinity / ( 1+0 ) == infinity

Answer 2

If x is greater than 4, sqrtx will be less than x/2, and therefore x-sqrtx will be greater than x/2. Now x/2 can be made arbitrarily large as you increase x, so your expression also gets arbitrarily large as x goes to infinity. Which is to say "the limit is infinity".

Answer 3

infinity

Answer 4

infinity

Answer 5

As x -> infinity, x-root(x) -> x
(since 'x' is 'bigger' than 'root(x) )
so x-root(x) also tends to infinity - you can test it out on your calculator, as x gets bigger, then the result just keeps on increasing!

Answer 6

actually, x does tend to infinity faster than root(x), but the limit is undefined, as inf - inf is an undefined quantity.