SOLUTION: without L'Hospitals rule prove that : limt(x^(1/x)) =1 (as x= 1)

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Question 1197557: without L'Hospitals rule prove that :
limt(x^(1/x)) =1 (as x= 1)
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

lim%28x-%3E1%2Cx%5E%281%2Fx%29%29=+1

to prove, just plug in the value x=1
lim%28x-%3E1%2Cx%5E%281%2Fx%29%29=1%5E%281%2F1%29=1

Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.
without L'Hospitals rule prove that :
limt(x^(1/x)) =1 (as x= 1)

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The L'Hospital's rule has no any relation to calculating this limit.


Show this my note to your professor and discuss it with him (with her).


Also, if you know the "composer" of this text, say "Hello" to him (to her) and tell him (or her)
that he (or she) is wrong, formulating the task this way.


On L'Hospital rule read and learn from this very authoritative and informative source
https://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule


Learn the subject from there.


Only mathematically illiterate person could formulate a problem in this way,
if to exclude the case, when his (or her) intention was to make the audience laugh.