The Limit of Ln

Calculus Level 2

lim x 0 + ln ( x ) = ? \large \lim_{x\to 0^{+}} \ln(x) = \, ?

0 0 1 1 -\infty \infty

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2 solutions

Ashish Menon
Mar 7, 2016

From this we can clearly see that the answer is -\infty

Supposing you drew the graph correctly, you mean.

Whitney Clark - 5 years, 3 months ago

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Yes , ofcourse

Ashish Menon - 5 years, 3 months ago

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The thing is, the fact needs to be proven with logic, not with graphs.

Whitney Clark - 5 years, 3 months ago

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@Whitney Clark All right as you say, but i wanted to see what response i would get for posting this type of answer. 9 upvotes and 1 crticize by you :P

Ashish Menon - 5 years, 3 months ago

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@Ashish Menon I'm just being honest. Math is proven with logic and not pictures.

Whitney Clark - 5 years, 3 months ago

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@Whitney Clark @Whitney Clark This is a legit solution. This is not a picture, but a graph. A lot of calculus problems can be solved using graphs.

EDIT: For example, this

Mehul Arora - 5 years, 3 months ago

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@Mehul Arora Thanks for supporting mehul

Ashish Menon - 5 years, 3 months ago

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@Ashish Menon I always take the side which I feel is correct, and in this case I'm sure :)

Mehul Arora - 5 years, 3 months ago

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@Mehul Arora :-) thanks again

Ashish Menon - 5 years, 3 months ago

@Mehul Arora Graphs are still not logic.

Whitney Clark - 5 years, 3 months ago

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@Whitney Clark Why not? Graphs can tell more than words. :-)

Ashish Menon - 5 years, 3 months ago

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@Ashish Menon I'm just saying, suppose the graph was drawn wrong? Besides, even pictures can be misleading, as the introduction to my advanced calculus text shows. It is "obvious" that x 100 \sqrt[100]{x} never reaches above the logarithm function, if looked at from a limited angle, but further investigation shows this is wrong.

Whitney Clark - 5 years, 3 months ago

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@Whitney Clark But, this is calculus level 2, so chill

Ashish Menon - 5 years, 3 months ago

@Whitney Clark Okay, I agree. But we can say that Graphing using computer programs works?

Graphs are completely logical I feel.

Mehul Arora - 5 years, 3 months ago

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@Mehul Arora Did you just say "feel"? Math and logic aren't about feelings.

Whitney Clark - 5 years, 3 months ago

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@Whitney Clark Honestly, The feelings you're talking about are completely absurd in our case. When you're saying that drawing graphs to solve a problem isn't a logical solution, I am sorry sir but you are mistaken :/

What I also know is that Graphs are logical. So implying logic again, If math can be solved by logic, and graphs are logical, So Math can be solved by Graphs. Graphs are integral to mathematics.

Mehul Arora - 5 years, 2 months ago

@Whitney Clark Yes, i appreciate it, thanks I will take care not to post such a solution next time. Please consider it this time. :-)

Ashish Menon - 5 years, 3 months ago

@Whitney Clark Limits problems can be better understood and solved using graphs than traditional algebraic methods.

Nihar Mahajan - 5 years, 2 months ago

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@Nihar Mahajan Thanks for supporting, Nihar :-)

Ashish Menon - 5 years, 2 months ago
Ben Champion
Mar 20, 2016

y = l n ( x ) y=ln(x)

e y = x e^y=x

It is clear that in order to get a small positive "crumb" for x, we need a very large negative number for y.

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