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

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) (Show Source): You can put this solution on YOUR website!

to prove, just plug in the value

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

~~~~~~~~~~~~~~~~~~~~~~

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.

RELATED QUESTIONS
without L'Hospitals rule prove that : limt(x^(1/x)) = 1 when (x →... (answered by ewatrrr,ikleyn)
find: limt(1^x) as... (answered by MathLover1)
if limt(((n+1)^x -n^x)/(n^99))=100 as x→ ∞ prove that... (answered by Alex.33)
Without using l�Hopital�s Rule or Series find Limit(((1+x)^(1/x)-e)/x) as... (answered by math_helper)
Without using L'Hospitals rule find : Limt((e^(17x)-17e^x +16)/(e^(16x)-16e^x+15)). as (answered by ikleyn)
Find: limt((2π/x) * (1/(sin((πx/(x - 1)))))), when (x→ + ∞) (answered by ikleyn)
Find : limt((floor(x/3)-1)/(x-3)) , when... (answered by ikleyn)
prove that (x-1)(x^8+x^7+x^6+...+1)=x^9-1 without multiplying out the... (answered by Fombitz)
Without solving the equation prove that x=-2. Equation 3(x-1)+2=5-x (answered by Alan3354)