help me find the lim | Mathematics | Page 1

random drum Jun 28, 2024, 11:02 AM

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i've been trying to find this lim for a while but i can't manage

deep inletBOT Jun 28, 2024, 11:02 AM

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random drum i've been trying to find this lim for a while but i can't manage

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orchid dock Jun 28, 2024, 11:30 AM

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random drum i've been trying to find this lim for a while but i can't manage

Would you be more at ease if you replaced x with n?

random drum Jun 28, 2024, 11:30 AM

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idk if itll make a difference

orchid dock Jun 28, 2024, 11:30 AM

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Just a general question, it's alright if it's not better

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It is useful to know that the limit of (1 + k/x)^x is exp(k)

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As x goes to infinity

random drum Jun 28, 2024, 11:31 AM

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yeah but i couldnt put that to use in this case

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basically i dont know where to start

orchid dock Jun 28, 2024, 11:32 AM

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The denominator first

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You can simplify it as x^x(1 + (2/x)^x)

random drum Jun 28, 2024, 11:32 AM

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oh

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well that's new let me check

orchid dock Jun 28, 2024, 11:32 AM

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So see that it is equivalent to x^x

random drum Jun 28, 2024, 11:37 AM

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yeah i dont think i have any idea of what i'm doing rn

orchid dock Jun 28, 2024, 11:37 AM

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Well you just factor x^x

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In the denominator

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It's like, a + b = a(1 + b/a)

random drum Jun 28, 2024, 11:38 AM

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doesn't that leave me with x^x in the denominator

orchid dock Jun 28, 2024, 11:38 AM

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No but it leaves you with x^x times something that converges to 1

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1 + (2/x)^x clearly converges to 1

random drum Jun 28, 2024, 11:40 AM

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yeah

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let me try something

orchid dock Jun 28, 2024, 11:40 AM

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Sure

random drum Jun 28, 2024, 11:41 AM

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i ended up with x^x * e^(2/x)^x, is that even logical

orchid dock Jun 28, 2024, 11:42 AM

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In the denominator?

random drum Jun 28, 2024, 11:42 AM

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yeah

orchid dock Jun 28, 2024, 11:42 AM

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No not really

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But i mean there is no need for further modifications

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You can leave it as x^x(1 + (2/x)^x)

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Now we move to the numerator

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Likewise you are going to factor x^x

random drum Jun 28, 2024, 11:43 AM

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we do the same thing with x^x?

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oh

orchid dock Jun 28, 2024, 11:43 AM

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And you will see the magic with exp

random drum Jun 28, 2024, 11:44 AM

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the x^x in the numerator goes with the x^x in the denominator

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we're left with (1+(3/x^x))^x

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minus the rest

orchid dock Jun 28, 2024, 11:44 AM

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No not quite

random drum Jun 28, 2024, 11:44 AM

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okay...

orchid dock Jun 28, 2024, 11:45 AM

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(1 + 3/x)^x - (1 - 3/x)^x

random drum Jun 28, 2024, 11:45 AM

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ohh

orchid dock Jun 28, 2024, 11:45 AM

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You factored wrong

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But now you know the limit of that

random drum Jun 28, 2024, 11:46 AM

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e^3 - e^-3

orchid dock Jun 28, 2024, 11:46 AM

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Correct

random drum Jun 28, 2024, 11:47 AM

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oh my god i had this answer 3 days ago but it was through bullshitting

orchid dock Jun 28, 2024, 11:47 AM

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I mean it's alright maybe you just needed better justification to convince yourself

random drum Jun 28, 2024, 11:47 AM

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thanks alot!

orchid dock Jun 28, 2024, 11:47 AM

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Np

random drum Jun 28, 2024, 11:48 AM

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+close

#help me find the lim