Question

Find the limit (if it exists).

lim as x approaches 0 of ( (4-sqrt(16 + h)) / (h) )

Answer 1

it exists all right. it is minus the derivative of
\[\sqrt{x}\] at x = 16, so it is
\[-\frac{1}{8}\]

Answer 2

\[\lim_{h \rightarrow 0} (4-\sqrt{16})\div h\]

Answer 3

have you covered derivatives yet?

Answer 4

No, that's the problem. This is chapter 2 and derivatives are chapter 4 I think.

Answer 5

if not then you have to do this:
\[\frac{4-\sqrt{16+h}}{h}\times \frac{4+\sqrt{16+h}}{4+\sqrt{16+h}}\]

Answer 6

Yup, that's what I did. I still managed to get 0 when putting 0 in for h...

Answer 7

16 - 16 - h / 4h + 4
^ = 0 - 0 / 4(0) + 4

Answer 8

you get
\[\frac{16-(16+h)}{h(4+\sqrt{16+h})}\]
\[=\frac{-h}{h(4+\sqrt{16+h})}\]
\[=\frac{-1}{4+\sqrt{16+h}}\]

Answer 9

now replace h by 0 to get your answer

Answer 10

Wow. OK, so I must have converted h to 0 way too early.

Answer 11

cancel it first! don't replace h by 0 until you have canceled it

Answer 12

That's what I get for rushing through the answer. I've gotten the problems before this one and the ones after this one finished, but this one was freaking killing me! Thanks a bunch, satellite73!

Answer 13

Yeah, that makes sense. That's what I meant...I had been replacing it before cancelling things out. ARGH! 20 minutes wasted, answer received in 3...dangit.

Answer 14

yw