# A hypothetical square grows at a rate of 16 m²/min. How fast are the sides of the square increasing when the sides are 15 m each?

The sides are increasing at a speed of

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To find the rate at which the sides of the square are increasing, you can use the formula for the rate of change of area with respect to time. Since the area ( A ) of a square is given by ( A = s^2 ), where ( s ) is the length of a side, the rate of change of area ( \frac{dA}{dt} ) is ( 2s \frac{ds}{dt} ), where ( \frac{ds}{dt} ) is the rate at which the sides are increasing.

Given that ( \frac{dA}{dt} = 16 , \text{m}^2/\text{min} ) and ( s = 15 , \text{m} ), you can solve for ( \frac{ds}{dt} ):

[ \frac{dA}{dt} = 2s \frac{ds}{dt} ] [ 16 = 2(15) \frac{ds}{dt} ] [ 16 = 30 \frac{ds}{dt} ] [ \frac{ds}{dt} = \frac{16}{30} = \frac{8}{15} , \text{m/min} ]

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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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