Math Help Please!! Limits question!?

Question

The question is to use the properties of limits to help decide whether the limit exists and find it's value if it does.

lim as x approches infinity

8x²- 8x^4
__________
5² - 6x - 6

The thing that i'm not sure about is, i think your supposed to devide everything by the highest exponant, but if you do that then the bottom is zero and then i don't know what that means. can anyone help? thanks

Answer 1

You should write it properly because you wrote 5² at the bottom and I guess it's 5x² instead. In this case it's quite simple. You cellect the x with maximum exponent and then consider that all terms with x at some exponent at denominator go to zero when x goes to ∞. So let's proceed this way:



lim(x→∞) x⁴*[8/x² - 8]/x²*[5 - 6/x - 6/x²] = lim(x→∞) x²*[8/x² - 8]/[5 - 6/x - 6/x²]



Like we said, when when x goes to ∞ all terms like 8/x², 6/x, etc. go to zero, so you're left with:



lim(x→∞) x²*[0 - 8]/[5 - 0 - 0] = lim(x→∞) x²*(-8/5) = -∞

Answer 2

umm... 2+2=5!



edit: 5 times squared minus 8 times something 4 over 5 squared minus 6 times minus 6...

uhh.. yupp you're screwed..

Answer 3

Go to Khan Academy, that'll help you for sure. It's online. :)