I can't figure out this one, its driving me crazy. My teacher made this problems up and he call them Interesting problems and sometimes even the tutors struggle with his problems.

Lim 5 + 2x^2 + x^3 / over 3 - x^2 + 2x^3

x->infinity

It has the sign of Infinity but i can't draw it and -> is an arrow as x approaches...

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Evaluate the limit and illustrate each step that involves the use of a limit property.

Lim t^3 - 3t^2 - t + 3 / over t^2 - t - 6

t->3

as t approaches 3

so far i have:

-> 27 - 27 - 3 +3 / over 9 - 3 - 6

-> 0 / over 0

= 0

I substitute it 3 for t but i don't know if this is the right way for this one, Also i need to illustrate each step that involves the use of a limit property, but how? Do i have to label each step like by hypothesis, by substitution, by arithmetic etc..?