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

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

x->0

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.

Calculus

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