Question

Solve for the limit two out of the three ways (numerically, analytically or graphically).. Problem is typed out as a comment

Answer 1

algebraically, you would multiply top and bottom by sqrt(4+x)+2 and that would let you get rid of the x on the bottom.

Answer 2

okay hold on, let me do that real fast

Answer 3

how do you multiply the top out? Im confused

Answer 4

and the bottom? Okay, the whole square root is confusing me

Answer 5

\[\frac{ \sqrt{4+x}-2 }{ x }=\frac{ (\sqrt{4+x}-2)(\sqrt{4+x}+2) }{ x(\sqrt{4+x}+2) }=\frac{ (\sqrt{4+x})^2-(2)^2 }{ x(\sqrt{4+x}+2) }=\frac{ 4+x-4 }{ x(\sqrt{4+x}+2) }\]
\[=\frac{ x }{ x(\sqrt{4+x}+2) }=\frac{ 1 }{(\sqrt{4+x}+2) }\]

Answer 6

okay, that makes sense. Now how do you finish it? I'm sorry. Im really lost when it comes to limits

Answer 7

are you there?

Answer 8

graphically is rather easy, just graph it and look where "x" is going
btw the website is getting a bit lagged, so you know, maybe pgpilot326 is just a big lagged

Answer 9

oh okay, thank you! Do you know how to finish the above part though?

Answer 10

which one?

Answer 11

the analytical one that they typed out

Answer 12

to take the limit, just plug in 0 for x