A Nice Limit to Tend

Calculus Level 3

Find the limit below.

lim ⁡ x → 0 + x ( x x − 1 ) \large \lim_{x\to 0^+} x^{(x^x-1)}


The answer is 1.

Rajyawardhan Singh by Rajyawardhan Singh , 19, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

lim ⁡ x → 0 + x x x − 1 = ( 0 + ) ( 0 + ) 0 + − 1 = ( 0 + ) 1 − 1 = ( 0 + ) 0 = 1 \displaystyle \lim_{x \to 0^+} x^{x^x-1} = (0^+)^{(0^+)^{0^+}-1} = (0^+)^{1-1} = (0^+)^0 = \boxed 1 .

0 Helpful 0 Interesting 0 Brilliant 2 Confused

Not sure if this is too picky or not, but I think that it's important to leave the + sign when you make a substitution of 0+ for x. The limit should be (0+)^(0+^(0+)-1) which is (0+)^((1+ )-1) = (0+)^(0+), which is 1.

Michael Boyd - 2 years, 4 months ago

Log in to reply

Yes, I was thinking how best to present it. I will change my solution.

Chew-Seong Cheong - 2 years, 4 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...