Question

LIMITS: Click to see question

Answer 1

\[\lim_{x \rightarrow \pm \infty} (x^4+x^3)/(12x^3+128)\]

Answer 2

divide top and bottom by x^3

Answer 3

we are dividing top and bottom by x^3
because the degree of the bottom polynomial is 3

Answer 4

\[\lim_{x \rightarrow \infty} \frac{\frac{x^4}{x^3}+\frac{x^3}{x^3}}{\frac{12x^3}{x^3}+\frac{128}{x^3}}\]

Answer 5

now figure out the limit for each of those mini-fractions

Answer 6

oh!i remember how to do this! one moment while i work it out, please?

Answer 7

\[(x+1)/(12+128/x^3)\]

Answer 8

and then replace x with 0, right?

Answer 9

i mean with infinity

Answer 10

right now you must look at x approaches infinity
and also x approaches -negative infinity

Answer 11

\[\infty+1/12+0\] ?

Answer 12

so you have infinity for x approaches infinity

ok now you need to evaluate your second question which involves x going to -infinity

Answer 13

ok, one moment

Answer 14

\[-\infty+1/12+0\] ?

Answer 15

right so you have:
\[\lim_{x \rightarrow \infty}\frac{x+1}{12+\frac{128}{x^3}} =\frac{\infty}{12+0}=\infty \\ \lim_{x \rightarrow -\infty} \frac{x+1}{12+\frac{128}{x^3}}=\frac{-\infty}{12+0}=-\infty\]

Answer 16

also I like to separate my numerators by doing ( )
and my denominators by doing ( )
like I would write what you said like (-infty+1)/(12+0)
it is more proper and correct :p

Answer 17

haha, okay! thank you so much!

Answer 18

np