Thread: Would like Help with Calc problem!

Here's the problem
limit (sqrt(x^2+5x)-x)
x->[infinity]

The answer is (according to two websites and my calculator) 5/2.

Here's the work I've done so far.

[Multiply the conjugate]
(sqrt(x^2+5x)-x)/1 * (sqrt(x^2+5x)+x)/(sqrt(x^2+5x)+x)

x^2+5x-x^2/(sqrt(x^2+5x)+x) = 5x/(sqrt(x^2+5x)+x)

and I don't know how to get farther than that. Please help!

Originally Posted by MisanthropicMan

Here's the problem
limit (sqrt(x^2+5x)-x)
x->[infinity]

The answer is (according to two websites and my calculator) 5/2.

Here's the work I've done so far.

[Multiply the conjugate]
(sqrt(x^2+5x)-x)/1 * (sqrt(x^2+5x)+x)/(sqrt(x^2+5x)+x)

x^2+5x-x^2/(sqrt(x^2+5x)+x) = 5x/(sqrt(x^2+5x)+x)

and I don't know how to get farther than that. Please help!

Continuing from where you left off:


Here is a nice little trick: factor out an x from the denominator:







As everything else is constant:



I trust you can continue from here?

Originally Posted by Gusbob

Continuing from where you left off:


Here is a nice little trick: factor out an x from the denominator:

Or, same thing, divide both numerator and denominator by x.

As everything else is constant:



I trust you can continue from here?