Infinity? Calc? Huh?

[horses48]

I am a college freshman taking calculus(yipppeeee!!! :roll: ) Yesterday my professor gave a lecture and I thought I understood what he was talking about, but I have no idea how to do this problem:

http://i490.photobucket.com/albums/rr26 ... l/yuck.jpg

I don't understand how to solve this. What I think I need to do is set f(x) > 5000 and try to isolate x. Then using that number adjust it so when you plug it into x it is just greater than 5000. The problem is....I don't know how to get x alone. I have tried several times and it still wont work. Am I thinking about how to do this problem wrong? Could someone explain how I can solve this? Thanks

 

[galactus]

You have the idea about the limit.

But to solve for x when L=5000

\(\displaystyle \frac{1}{(1-x)^{6}}=625\)

\(\displaystyle (1-x)^{6}=\frac{1}{625}\)

\(\displaystyle 1-x=(\frac{1}{625})^{\frac{1}{6}}\)

\(\displaystyle x=\frac{5^{\frac{1}{3}}}{5}+1, \;\ x=1-\frac{5^{\frac{1}{3}}}{5}\)

Find the decimal approximation and you should be able to find the value of delta by seeing how far on either side of 1 the two values fall.

Plus, here is a site that explains it pretty well.

http://www.math.jmu.edu/~taal/235_2000p ... ndelta.pdf