# How do you find the limit #(x^(1/4)-1)/x# as #x->1#?

The limit is

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To find the limit of (x^(1/4)-1)/x as x approaches 1, we can use algebraic manipulation and the limit laws.

First, we simplify the expression by multiplying the numerator and denominator by the conjugate of the numerator, which is (x^(1/4)+1). This allows us to eliminate the square root in the numerator.

(x^(1/4)-1)/x * (x^(1/4)+1)/(x^(1/4)+1) = (x-1)/(x * (x^(1/4)+1))

Next, we can substitute x=1 into the expression:

(1-1)/(1 * (1^(1/4)+1)) = 0/2 = 0

Therefore, the limit of (x^(1/4)-1)/x as x approaches 1 is 0.

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