According to my calculations, you do not need to use L'Hopital here.Find lim ((ln6x)^2)/(ln2x)^2 as x approaches infinity. So we get infinity over infinity but applying L'Hopitals Rule I get the same over and over again. The answer should be 9. Can you spot the mistake?
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First, what you claim to be doing (first and second derivatives of y) is neither what L'Hopital calls for, nor what you did! The rule is to differentiate the numerator and the denominator separately, which you did.
But why did you rearrange the expression, complicating it more, before doing that? Just differentiate the numerator and the denominator of the original expression! You will get the correct limit without much trouble; but it is 1, not 9.
(I'm assuming you are required to use L'Hopital, since it is not the only way.)
There's got to be the mistake in the keys then... In WolframAlpha, which I don't like to use tho, I also got 1. Thank you for your time and effort spent to help me!!According to my calculations, you do not need to use L'Hopital here.
[ln(6x)/ln(2x)]2 = [{ln(3) + ln(2x)}/ln(2x)]2 = [1 + ln(3)/ln(2x)]2
However, I am getting a limit of 1.
I did a spreadsheet calculation and saw the limit approaching 1 - very slowly.
At x =500000, I get
[ln(6x)/ln(2x)]2 = 1.165363882
At x =1000000, I get
[ln(6x)/ln(2x)]2 = 1.157175998
slowly decreasing and nowhere near 9!!
But not me, I LOVE to complicate stuff)Recall that A2/B2= (A/B)2.
I would have computed the lim for (A/B) and then squared the result simplifying the problem significantly.
Have you heard of Algebraic Topology? That stuff will make you smile all day long and you won't have to make it complicated as it always is!But not me, I LOVE to complicate stuff)
thanks)
I've heard of it but only that 'A doughnut is the same as a cup in that thing'Have you heard of Algebraic Topology? That stuff will make you smile all day long and you won't have to make it complicated as it always is!
Actually what you mentioned is just topology, algebraic topology is way for fun then just plain ole topology. You'll be talking to yourself on the street corner after just a week of studying this material.I've heard of it but only that 'A doughnut is the same as a cup in that thing'
And since I've started learning maths in a normal way (mainly thanks to you guys), which doesn't include only learning formulas by heart, not a long time ago, I have a lot of stuff yet to learn. But I already love it from your description! I'll make sure I check it out))
looks like something that makes you immortal after you finish the courseActually what you mentioned is just topology, algebraic topology is way for fun then just plain ole topology. You'll be talking to yourself on the street corner after just a week of studying this material.
Heck, when I go out to study I usually sit at the bar in a restaurant and mumble at my calculations. I've started being preemptive and tell anyone sitting next to me that, yes, I did take my medications today!Actually what you mentioned is just topology, algebraic topology is way for fun then just plain ole topology. You'll be talking to yourself on the street corner after just a week of studying this material.
When the blue-tooth speakers first came out - I felt the number of "algebraic topologists" suddenly jump. I found whole bunch of people walking on the side-walk laughing, arguing, with "no-body" there!!Actually what you mentioned is just topology, algebraic topology is way for fun then just plain ole topology. You'll be talking to yourself on the street corner after just a week of studying this material.