(Please think of a pun for LIMIT yourself) #2

Calculus Level 2

$\Large { \lim \limits_{(x,n) \to (\infty,0)} {x}^n } = ?$

0

\ln(2)

1

e

Limit does not exist.

1 solution

Anh Khoa Nguyễn Ngọc
Aug 14, 2020

The given limit lead to $∞^{0}$ , which is one of seven indeterminate forms of limit.

More at Wikipedia Indeterminate form .

I think only two of them can be found using L'Hopital, others can't be, and $\infty^0$ can't be.

Vinayak Srivastava - 10 months ago

Not just 2. it depends if the function can be rearranged into a $\cfrac{0}{0}$ or a $\cfrac{\infty}{\infty}$ indeterminate form. for example: $\lim\limits_{x\to 0} -x\ln x$ is a $0 \cdot \infty$ indeterminate form but it can be solved with some rearranging for the L'Hopital's rule to be available. in fact, the wikipedia page that is linked has some transformations for other indetermiante forms so that they can be L'Hopital Rule "friendly"

James Watson - 10 months ago

For the limit pun, how about:

Anatomy's the LIMIT?

I am not that good when it comes to puns...

Yajat Shamji - 10 months ago

(Please think of a pun for LIMIT yourself) #2

1 solution

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