Bernoulli's Rule

Question

Bernoulli's Rule

agent_a · Answer

attachment

amistre64 · Answer

do you recall the indeterminant forms?

amistre64 · Answer

i believe a can be factored and therefore turned into a fraction ...

b seems a little more thought provoking to me

agent_a · Answer

Yes I solved part a, but I keep ending-up at the Indeterminant Form. It seems to never end.

amistre64 · Answer

:)

amistre64 · Answer

$$\sqrt{x^2+x}-\sqrt{x^2-x}$$
$$\sqrt{x(x+1)}-\sqrt{x(x-1)}$$
$$\sqrt{x}(\sqrt{x+1}-\sqrt{x-1})$$
$$\frac{\sqrt{x+1} - \sqrt{x-1} }{1/\sqrt{x}}$$
is that your approach?  ofsomething else

agent_a · Answer

On another website, I asked other people to help me out with the same question. However, I got two different answers for both who responded. As for myself, I only managed to solve part a, and my answer was different from both of those who solved the problem. My answer for part a was just perpetual indeterminate forms, which is why I decided to stop. As for the other two, they beg to differ...

Which of these answers would you agree with the most?

amistre64 · Answer

the top limits to zero, not 2:

sqrt(inf^2) - sqrt(inf^2) = 0  by sloppy reasoning alone

amistre64 · Answer

and the second one limits to 1:  same limit as 0^0 by sloppy logic too

agent_a · Answer

For both occasions, which ones are you referring to?

amistre64 · Answer

well, the first one got b right, and the second one got a right :)

agent_a · Answer

Ahhhh

amistre64 · Answer

so im split 50-50

agent_a · Answer

Okay I see now.

agent_a · Answer

Thanks!

amistre64 · Answer

good luck

amistre64 · Answer

a: http://www.wolframalpha.com/input/?i=limit%28x+to+1%5E%2B%29+%28x-1%29%5E%28lnx%29 b: http://www.wolframalpha.com/input/?i=limit%28x+to+1%5E%2B%29+%28x-1%29%5E%28lnx%29

amistre64 · Answer

odd, those links should be different ... oh well.  give wolf a try for dbl chks :)

agent_a · Answer

-______- Why didn't I think of putting the whole equation in to check....  

Thanks again!