Basic Limit Q

[ugly_boy]

I have a pretty basic question:

How do you solve a limit if the f(x) is a fraction and has a square root in the numerator, without using the quotient rule, for instance:

limx→2[√(x) - 2/(2x+5)]

Thanks.

Comments

[where_was_i]

There're really not any tricks to this unless the value you're approaching does something weird (like the negative of a square root). You find this limit just like you would any other limit. That is: you plug in the value you are approaching and simplify. Remember, what you're doing is looking at the graph of f(x) and asking what value it looks like f(x) approaches as x approaches 2. This might be a somewhat funky graph, but it goes without doubt to (√(2)-2)/9 as x goes to 2.

[joshua_green]

Plugging in the value you're approaching works provided that the function you're dealing with is continuous.

[ugly_boy]

And provided that it's a polynomial, correct?

[joshua_green]

Continuity suffices.  All polynomials are continuous.