Question

someone please explain to me how to go about this....question in comments

Answer 1

Find the limit or show that it does not exist:\[\lim_{x \rightarrow \infty} ( \sqrt{x ^{2}+ax}-\sqrt{x ^{2}+bx} )\]

Answer 2

Please

Answer 3

i dont know im not sure

Answer 4

thanks though

Answer 5

i have reached at \[\frac{ a-b }{ 2}\]

Answer 6

multiply and divide by the conjugate , you have an indeterminant form as it is

Answer 7

\[\lim_{x \rightarrow \infty}[\frac{ \sqrt{x^2+ax}-\sqrt{x^2+bx} }{ 1 }*\frac{ \sqrt{x^2+ax}+\sqrt{x^2+bx} }{ \sqrt{x^2+ax}+\sqrt{x^2+bx} }] = \]

Answer 8

\[\frac{ ax - bx }{ \sqrt{x^2+ax}+\sqrt{x^2+bx} }\]

Answer 9

\[\lim_{x \rightarrow \infty}\frac{ a - b }{ \sqrt{1 + \frac{ a }{ x }}+\sqrt{1+\frac{ b }{ x }} }\]

Answer 10

right (a-b)/2

Answer 11

a/x and b/x go to zero as x goes to infinity

Answer 12

@mokeira

Answer 13

factor x from the top, and factor x^2 in each root term, and pull out the x from each root then, cancel, left with that limit, which goes to (a-b)/2

Answer 14

In case you don't see what i did, here it is, this process for each root

\[\sqrt{ x^2+ax} =\sqrt{ x^2*(1+\frac{ a }{ x })} = x*\sqrt{1 + \frac{ a }{ x }}\]

Answer 15

Thank you for your explanation @DanJS