# How do you find a positive number such that the sum of the number and its reciprocal is as small as possible?

The smallest sum of a number

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To find the positive number ( x ) such that the sum of the number and its reciprocal is as small as possible, you need to minimize the expression ( x + \frac{1}{x} ). This is done by finding the critical points of the function and determining whether they correspond to a minimum. To do this, you can take the derivative of the expression with respect to ( x ), set it equal to zero, and solve for ( x ). After finding the critical points, you can use the second derivative test to determine whether they correspond to a minimum or maximum. Alternatively, you can complete the square to find the minimum value. The result will be ( x = 1 ), which corresponds to the minimum sum of the number and its reciprocal.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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