Question

lim as x approaches infinity (1+3/x)^(5x)

Answer 1

1 becuase as x approach infinity the 3/x goes to zero which just leaves 1^(infinity) and 1 to any power is 1

Answer 2

Okay well it says that the answer is e^15 .. how is that?!

Answer 3

\[\lim_{x \rightarrow \infty} (1+{3\over x}^{5x})\]is that what it is?

Answer 4

ops, typo

Answer 5

the exponent should be out of the parenthesis

Answer 6

Yes that is right besides the exponent outside of the parenthesis

Answer 7

hmmm....definitely looks like 1 to me

Answer 8

Yeah I wasn't sure how they got e^15. I don't understand at all

Answer 9

the answer is e^15 but i'm not sure how to get there

Answer 10

e^(5/3)

Answer 11

i mean e^(15) sorry

Answer 12

how did yu get there myininaya ?

Answer 13

recall limit x->infinity (1+1/x)^x=e

Answer 14

Is that something I should know off the top of my head?

Answer 15

i guess lol
i just recalled it though like a memory
or you know lim x->0 sinx/x=1
or some property like that

Answer 16

oh boy.. i never liked limits anyways.. lol

Answer 17

good catch myininaya
thats just one of those weird math things

Answer 18

Okay I remember the sinx/x = 1

Answer 19

So where did the 15 come from

Answer 20

from the 3/x instead of 1/x and the power of 5x instead of x

Answer 21

http://answers.yahoo.com/question/index?qid=20110223065841AAHpCSc

Answer 22

they show that lim x-> infinity (1+a/x)^x=e^a
so if we have lim x-> infinity (1+3/x)^x=e^3
and if we have lim x-> infinity (1+3/x)^(5x)=lim x->infinity [(1+3/x)^x]^5=
(the inside goes to e^3) = e^[3(5)]=e^15

Answer 23

Okay that makes sense now

Answer 24

Thank you so much!

Answer 25

np

Answer 26

catherine you can also see if we plug in really big values for x (1+1/x)^x is getting closer to e

Answer 27

Which is why it comes to e in the above limits?

Answer 28

yes you do that for any function
you can plug values in for whatever x is getting closer to to see where the function is getting closer to as x gets closer to whatever number its approaching