Question #9d392

1 Answer
Dillin N.
Dec 9, 2017

The #limx rarr 0# does not exist as

#lim x rarr 0^+ ((2^-x - 10^x)/2)^(1/x)# yields 0

while

#lim x rarr 0^(-) ((2^-x - 10^x)/2)^(1/x)# yields #oo#

Explanation:

Graphing #((2^-x - 10^x)/2)^(1/x)# we can side as the function approaches 0 from the left it goes to infinity while on the right side it approaches 0. Because the LHL #!=# RHL the limit at x = 0 does not exist.

graph{((2^(-x) - 10^(x))/2)^(1/x) [-10, 10, -5, 5]}

You can also use a tabular method of inserting numbers from the left such as -.00000000000001 and from the right such as .00000000000001 and you'll see they do not approach the same values.

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