Hello!Can you tell me how to calculate the following limit:

lim  {[sqrt(x+1)]^(1/n)}/x,where n is a positive integer.

PS I need the method rather than the answer.Thanks.

The number n is positive, so the power is positive.
Put in 0 for x.

The top of the fraction becomes {[sqrt(0+1)]^(1/n)}.
Since 0+1 is 1, this is {[sqrt(1)]^(1/n)}.
Since sqrt(1) = 1, this is 1^(1/n).
Since n is not zero { in fact, it is positive }, this is 1.

If we put x=0 in the denominator, we get 0.

Since we have 1/0, and that is undefined, that's what the value of the limit is.

You said you already got this, though, so just take the text of the start of this answer.


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