Limit #1

Calculus Level 3

lim ⁡ x → 0 + x x = ? \large \lim_{x \to 0+} x^x = ?

n n None of the others 1 0 ∞ \infty

Genius Harith by Genius Harith , 16, India

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2 solutions

Genius Harith
Oct 28, 2018

Sorry for improper image. Hope you can zoom.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

The correct answer to the question is: Limit does not exist.

If x is slightly greater than zero, the limit tends to 1. If it x is less than zero, the limit is no longer a real number.

Left hand limit is not equal to the right hand limit and hence, it does not exist.

Although the solution does show that x is slightly positive, the question does not indicate this.

Cheers!

Karan Chatrath - 2 years, 7 months ago

Maybe but even mine is correct

Genius Harith - 2 years, 7 months ago
Parth Sankhe
Oct 29, 2018

If L = l i m x → 0 x x L=lim_{x\rightarrow0}x^x , then l n ( L ) = l i m x → 0 x l n ( x ) ln(L)=lim_{x\rightarrow0}xln(x) . The limit xlnx can easily be solved using L'Hospitals method, and it comes out to be 0.

Thus L=1.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Yep but not Always

Genius Harith - 2 years, 7 months ago

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