Limits

Calculus Level 3

Find lim x 0 ( 34 3 x + 219 7 x + 685 9 x 3 ) 1 x \displaystyle \lim_{x \rightarrow 0} \left (\frac{343^x + 2197^x + 6859^x}{3}\right)^{\frac{1}{x}}

Try to find the answer without L'hopital's rule.


The answer is 1729.

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2 solutions

Abhishek Sharma
Feb 16, 2015

I am writing basic hint not the complete solution. Manipulate the expression to use the formula concerning (1+x)^(1/x). After that in the exponent you could use identity concerning (a^x-1)/x.

Lu Chee Ket
Feb 13, 2015

Would you mind elaborating your solution? Thanks.

Siddhartha Srivastava - 6 years, 4 months ago

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Please explain your reason of adjusting usual 100 points to 10 points. The proof I obtained (not shown here) is the proof. You may like to keep this implicit.

Lu Chee Ket - 6 years, 4 months ago

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Please explain your reason of adjusting usual 100 points to 10 points.

I'm not sure what you mean. I didn't do anything to change the points.

Siddhartha Srivastava - 6 years, 4 months ago

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@Siddhartha Srivastava You mean the system made it 10 points. Do you see it?

Lu Chee Ket - 6 years, 4 months ago

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@Lu Chee Ket Yes, I see it. But how do you change the points from 10 to 100? I didn't do anything different while posting the question.

Siddhartha Srivastava - 6 years, 4 months ago

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@Siddhartha Srivastava All right. Do you prefer to keep the answer implicit or just let me to write here? Since I think this is a bit special, we preserve no confidential thing then.

Lu Chee Ket - 6 years, 4 months ago

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@Lu Chee Ket Its up to you. I had asked for a solution because the solution you have given isn't that obvious.

Siddhartha Srivastava - 6 years, 4 months ago

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@Siddhartha Srivastava Let's keep this as confidential.

Lu Chee Ket - 6 years, 3 months ago

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