A useful tool for some limits is:
Using this on your limit, we get:
How do I go about solving this kind of limit?
Do I handle each part individually?
The only thing I can think about, is taking the derivative of each part.
To me, this still looks like it is undefined..
Can someone please explain how to do these types? Perhaps a link to a tutorial too. I'm not sure what to search online for these types either. Do they have a special name?
Thanks!
Thank you!
So, since the limit of f(x) =0, we can ignore whatever the limit of g(x) is, since we are multiplying. But for this scenario, would it be safe to say that the limit of g(x) would have been undefined? In that case 0 * undefined = 0?
Thanks for that tool!
However, did you mean to say:
did you have the 0 & infinity symbols backwards?
Ok IC. So for
It would be the same as: Lim f(x) - Lim f(g)
so for:
x becomes really close to one, making ln(x) extremely small. Then 1/rly small = rly big and approaches infinity?
Same with the other term:
[tex]
\displaystyle \lim_{x \to 1^{+}} \frac{1}{x-1} = \infty
[/tex]
because x-1 will approach a super small number, and the reciprocal of that will be a rly big number, approaching infinity.
So, then we have infinity-infinity = 0?
But this appears to be wrong. What is wrong with my reasoning?