Determine lim x->0+ sqrt(x)/x.

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Multiple Choice

Determine lim x->0+ sqrt(x)/x.

Explanation:
The behavior being tested is how a quotient behaves when the denominator approaches zero from the positive side. Here, sqrt(x)/x can be rewritten as 1/sqrt(x). As x approaches 0+ the square root tends to 0, so its reciprocal grows without bound. Since everything is positive near 0+, the limit goes to +infinity. It’s not a finite value, and not negative infinity, because the expression stays positive and increases without bound as x gets smaller.

The behavior being tested is how a quotient behaves when the denominator approaches zero from the positive side. Here, sqrt(x)/x can be rewritten as 1/sqrt(x). As x approaches 0+ the square root tends to 0, so its reciprocal grows without bound. Since everything is positive near 0+, the limit goes to +infinity. It’s not a finite value, and not negative infinity, because the expression stays positive and increases without bound as x gets smaller.

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