Find order relation

Calculus Level 3

Find the order relation of the following limit values: A = lim ⁡ x → ∞ x e x B = lim ⁡ x → ∞ ln ⁡ x x C = lim ⁡ x → + 0 x ln ⁡ x D = lim ⁡ x → + 0 x x . \begin{aligned} A &= \lim_{x\rightarrow \infty}\frac{x}{{e}^{x}} \\ B &= \lim_{x\rightarrow \infty}\frac{\ln{x}}{x} \\ C &= \lim_{x\rightarrow +0} x\ln{x} \\ D &= \lim_{x\rightarrow +0} {x}^{x}. \end{aligned}

A=B<C<D A=B=C<D A<B=C<D A=B=C=D

View wiki
Srinivasa Satti by Srinivasa Satti

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

Vishal Sharma
Apr 13, 2014

To be more precise 'A' & 'B' approach zero from the positive side but 'C' approaches zero from the negative side. Therefore it should have been : " D>A=B>C "

2 Helpful 0 Interesting 0 Brilliant 0 Confused

This isn't really true. A limit simply assigns a number and as far as the arithmetic is concerned, there is no difference between approaching it from below or from above. If a limit is 0, it is 0.

Leonel Castillo - 3 years, 4 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...