Question

limit xapproaches infinity right side of x ^ sqrt x

Answer 1

anybody

Answer 2

what does the exponent approach as x goes to 0 ?

Answer 3

exponent is square root x variable on a variable

Answer 4

and in the limit that variable's value is what?

Answer 5

both should be approaching infinity

Answer 6

oh sorry, misread the q

Answer 7

RIGHT SIDE there is a plus

Answer 8

um... how do you approach infinity from the right????
that makes no sense...

Answer 9

\[\lim_{x \rightarrow x}x ^{\sqrt{x}} = \infty\]

Answer 10

Or did you mean negative infinity? than it's 0.

Answer 11

if it was \(\lim_{x\to\infty}x^{\sqrt x}\) that would be \(\infty\), but what does \(\lim_{x\to\infty+}x^{\sqrt x}\) even mean?

Answer 12

ok but how did you get there is it with e- no not negative looks like first response from zim

Answer 13

this?? \[\large\lim_{x\to\infty^+}x^{\sqrt x}\]

Answer 14

yes

Answer 15

or\[\large\lim_{x\to\infty^-}x^{\sqrt x}\]or\[\large\lim_{x\to-\infty}x^{\sqrt x}\]???
all mean different things. First one, \[\large\lim_{x\to\infty^+}x^{\sqrt x}\]has no meaning, because you cannot approach infinity from the right

Answer 16

wow

Answer 17

the book gives e^ infinity equals infinity

Answer 18

\[\large\lim_{x\to\infty}e^{\sqrt x}=\infty\] because x increases without bound forever, but \[\large\lim_{x\to\infty^+}x^{\sqrt x}\] means nothing because it makes no sense to come at positive infity from the right. infinity is the largest "number"; how can you approach the largest number from a larger number? that's a contradiction

Answer 19

caveat: infinity is not really a number

Answer 20

THANKS that does make sense

Answer 21

happy to help :)

Answer 22

I'm going to close this question and ask another in a few mins.

Answer 23

I may or may not be here