Question

Algebra/Calculus: g(x)= x^5-32/ x^3-8; find lim g(x) as X approaches 2. Seems simple enough but I got 8 as my answer but Mathematica says its 20... where did i mess up? Don't laugh, I'm not good in math :(

Answer 1

Well, the top and bottom are definitely going to share a factor because 32 to the 5th root is 2 and 8 to the 3rd root is also 2. So both the top and bottom have an (x-2) factor that can be canceled out. You just have to do some division to see what is left behind afterwards. By difference of cubes factoring, the bottom will look like (x-2)(x^2+2x+4). The top portion, just do long division, x^5-32/x-2. Once you do that, then youll be able to cancel out x-2 factors and see if you can plug in 2 into the results.

Answer 2

Lookslike the 20 mathematica gave you is only half correct.

Answer 3

I will go back and check my inputs, it may have been an error on my part. Thank you Psymon

Answer 4

Yeah, np :3

Answer 5

show us what you typed in mathematica

Answer 6

I input the function 1st : g[x_]:=x^5-32/x^3-8
Then I gave the command for the limit : Limit[g[x], x->2] nincompoop

Answer 7

there's something off with the notation

Answer 8

Either way, no need to use a math program. When you do long division on the top and difference of cubesthe bottom you get:

\[\frac{ (x ^{4}+2x ^{3}+4x ^{2}+8x+16)(x-2) }{ (x-2)(x ^{2}+2x+4) }\]
Thats just me factoring out the (x-2) common factor we know we have. So cancel out those two common factors and plug in your limit.

Answer 9

http://mathworld.wolfram.com/notebooks/Calculus/Limit.nb

Answer 10

Thanks you guys....

Answer 11

Np

Answer 12

x^5-32/x^3-8
fix to: (x^5-32)/(x^3-8)

Answer 13

my school requires me to use Maple, and that started to confuse me with syntax between Mathematica and Maple
it is annoying

Answer 14

I just figured this out, thank you for the help! These programs are very annoying