Find #lim_(x rarr oo) sqrt(x)/root3x# ?

Question

#lim_(x rarr oo) sqrt(x)/root3x#

Solution will be infinite, but how to solve this?

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Answer 1 · 2017-10-10T17:07:13

You can write the square root as the #1/2# power and the cube root as #1/3 power.
Division is the same as the difference between the two exponents.

Given: #lim_(x rarr oo) sqrt(x)/root3x#

You can write the square root as the #1/2# power and the cube root as #1/3 power:

#lim_(x rarr oo) x^(1/2)/x^(1/3)#

Division is the same as the difference between the two exponents.

#lim_(x rarr oo) x^(1/2-1/3)#

This does little good, because the limit remains unbounded:

#lim_(x rarr oo) x^(1/6)#