Make a table of values for the function and use the result to estimate the limit. lim as x approaches -2 with the function being ((x^3)+8)/(x+2). It seems very apparent to me that the limit would be -2, but when I plug in x values (for the table) of -2.1 -2.01 -2.001 -1.999 -1.99 -1.9 then the y values are "limited" at 12. Y values being 12.61 12.06 12.006 11.994 11.94 11.41. That kind of makes sense because the graph for x=-2 would be y=12 but x can not equal -2. So did I do this problem right with the answer being 12 and I am just over-thinking it? Or am I missing this completely ?

Question

anonymous · Answer

easiest thing to do is to factor the numerator as the sum of two cubes and cancel the common factor of $x+2$ then replace $x$ by $-2$

allank · Answer

Hmm, well, what you want is to estimate the value if y, when x is -2. From you're table, check out the trend of y as x approaches -2. Don't over-think it. Here is my sample as x approaches 0. 
x: -1 -.1 -.01 -.001 +.001    +.01 +.1
y:  4    3    3.5   3.55    3.55    3.5    3 
From this data, we see that y approaches something like 3.60. @satellite73 is showing you the algebraic, method.

anonymous · Answer

you get $$x^2-2x+4$$ and at $a=-2$ you in fact get $4+4+4=12$

anonymous · Answer

the answer to your question is 
Yes, you are right.

anonymous · Answer

Thank you

allank · Answer

You're welcome.