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Question
how do i go about answering this? I thought that factoring would be involved but how do i go about factoring the top to (x-6)?

lim    (x^3-9x^2+23x-30)/(x-6)
x->6

Answer
(x^3 - 9x^2 + 23x - 30)/(x - 6)

i'd use synthetic division

6`|`1`-9``23``|`-30
``|````6`-18``|``30           
--------------------
``|`1`-3```5``|```0

so when you divide (x^3 - 9x^2 + 23x - 30) by (x - 6)

you get

x^2 - 3x + 5 as your result.

as far as using limitations, i'm not certain since i've never done limitations.

but your y-value would be y > 23

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