Help in Infinite Limits Please

[Radge_AdDU]

Good day to all. Im new in this site . By the way, im very confused about the infinite limits, especially about one problem :3. Ive been using my Leithold TC7 for reference and study. Ive come to a problem, lim[(2/t^2+3t-4)-(3/t+4)] as t approaches -4 from the left. When I used the Limit theorem here in the book, my answer is wrong . It states here that when ever my numerator is greater than 0 and the denominator is 0, and it approaches 0 from negative values, then it's limit is NEGATIVE INFINITY. BUUUUUT!,,, when I checked, it was positive infinity . I performed the second way, in which I used -4.1 as my t, and it resulted to positive infinity.

so basically my question is, should you always perform the 2 ways to find the limit so that you will be certain of the answer? Thanks.

 

[stapel]

...im very confused about the infinite limits, especially about one problem.... Ive come to a problem, lim[(2/t^2+3t-4)-(3/t+4)] as t approaches -4 from the left. When I used the Limit theorem here in the book, my answer is wrong.

What answer did you get? What were your steps? (We cannot find errors in work that we can't see.)

It states here...

What "states"? Where? (We can't see what you're looking at and/or we can't hear whoever you're talking with.)

...that when ever my numerator is greater than 0 and the denominator is 0, and it approaches 0 from negative values, then it's limit is NEGATIVE INFINITY.

Unlikely. We'd need to see specifics of whatever discussion you're referencing.

I performed the second way...

You "performed" what? What is "the second way"? (What is "the first way"?)

...it resulted to positive infinity.

What "resulted to positive infinity"? What does it mean to "result to"?

First, let's clarify what the expression is. Is your limit statement as follows?

. . . . .\(\displaystyle \lim_{t \,\rightarrow\, -4^{-}}\, \left[\left(\dfrac{2}{t^2}\, +\, 3t\, -\, 4\right)\, -\, \left(\dfrac{3}{t}\, +\, 4\right)\right]\)

When you reply with confirmation or correction, please include a clear listing of your efforts so far. Thank you!