Problem by Manoj khatri!

Calculus Level 2

It is a common calculus question to find that lim ⁡ x → 0 + x x = 1. \displaystyle \lim_{x\to 0^+} {x^x} = 1.

Must it be true that lim ⁡ x → 0 + lim ⁡ y → 0 + x y = 1 ? \displaystyle \lim _{x\to 0^+} \lim_{y\to 0^+} x^y=1?

Yes No

Naren Bhandari by Naren Bhandari , 21, India

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1 solution

Suhas Sheikh
Jun 16, 2018

X and y can be varied independent of each other Hence nothing can be commented about the limit

4 Helpful 1 Interesting 0 Brilliant 0 Confused

I think the answer should be 1. A very small quantity raised to a very small power approaches unity regardless of how we label the variables. Ed Gray

Edwin Gray - 2 years, 11 months ago

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