Question

lim x^3 - (X^2/92x+1)
X-->-(1/2) please help Ive been stuck on this question for along time

Answer 1

this is what I interpreted:
\[\lim_{x \rightarrow -0.5} x^3-{{x^2} \over {92x+1}}\]
if it is this case, then just substitute x = -0.5
I got an answer -43/360

Answer 2

sorry missed the typo its X^2/(2x+1)

Answer 3

I can break it down to ((X^2)(2x-1)(x+1))/(2X+1) but then i get stuck

Answer 4

This limit diverges to negative infinity. You sure you are writing this right?

Answer 5

\[\lim_{x \rightarrow -1/2}x^3-\frac{x^2}{2x+1}?\]

Answer 6

yes but it wouldnt suprise me that the teacher gave out a typo, he has done it many times before

Answer 7

Also, I should say that this function has a vertical asymptote at x = -1/2

Answer 8

okay so then the limit is non existent then I should have seen that in my graph but looking at it now I miss typed it in there to thank you

Answer 9

Ok
first separate the easy things out
\[\=lim_{x \rightarrow -0.5} x^3-\lim_{x \rightarrow -0.5} {{x^2} \over{2x+1}}\]
Substitute the one term and apply long divison
\[=-0.125-[{x \over 2}-{x \over {2(2x+1)}}]\]
now the limit is pretty easy, divide top and bottom by x
\[=-0.125-0.25 +\lim_{x \rightarrow -0.5} {x \over {4x+2}}\]
\[=-0.375 +\lim_{x \rightarrow -0.5} {x \over {x(4+{2 \over x})}}\]
now cancel and substitute
\[=-0.375 + {1\over4+4} \]
\[=-{1 \over 4}\]