Question

\[\lim_{z \rightarrow 0} \frac{1}{\sqrt[z^{2}]{e}}\]

Answer 1

\[\Large \lim_{x \rightarrow 0} (\frac{1}{e^{1/x^2}})\]

Answer 2

use l'hospital

Answer 3

I learned limits for the first time this week...I don't know what l'hospital is

Answer 4

hmm okay...uhmm...

Answer 5

I don't understand how you can take a zeroth root of something

Answer 6

Or a fractional root of something

Answer 7

Hurts my head

Answer 8

try substituting 0 into \[\frac{1}{e^{1/x^2}}\]
what do you get?

Answer 9

Undefined

Answer 10

have you already discussed that \[\frac{1}{0} = \infty?\]

Answer 11

No, I only know \frac{1}{0} is undefined

Answer 12

Okay, this is making me believe I wrote down the wrong homework numbers and I'm doing the incorrect exercises...

Answer 13

How can I solve this with methods we haven't learned in class yet

Answer 14

well i dont know what you have learned do i

Answer 15

@lgbasallote \(1/0 \) is NOT defined. The LIMIT as x goes to zero of 1 / x is + infinity from the left (from numbers greater than zero) and - infinity from the right (numbers less than zero).

Answer 16

This is a very very very important notion in calculus. Evaluating a function at a point and taking the limit as it approaches that point are not always the same. :)

Answer 17

hmm good point

Answer 18

that's also the reason why i hate limits lol

Answer 19

I thought limit values are not allowed to be infinity?

Answer 20

I highly recommend (to anyone studying limits) to read this excellent set of notes from PSU (my undergrad university) :)


"relative rates of growth"

PDF
http://www.math.psu.edu/files/141rates1.pdf

Answer 21

Thank you mathteacher1729