# A rectangle's base remains 0.5 cm while its height changes at a rate of 1.5 cm/min. At what rate is the area changing, in cm when the height is 1.5 cm?

The area of the rectangle is changing at

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To find the rate at which the area is changing when the height is 1.5 cm, we use the formula for the area of a rectangle, which is given by length multiplied by width (base multiplied by height).

Given: Base (b) = 0.5 cm Height (h) = 1.5 cm Rate of change of height (dh/dt) = 1.5 cm/min

We are asked to find the rate of change of area (dA/dt) when the height is 1.5 cm.

Using the formula for the area of a rectangle:

A = b * h

We differentiate both sides of the equation with respect to time (t):

dA/dt = (db/dt) * h + b * (dh/dt)

Since the base remains constant, db/dt = 0.

Substituting the given values:

dA/dt = 0 * 1.5 + 0.5 * 1.5

Solving this:

dA/dt = 0 + 0.75

Therefore, when the height is 1.5 cm, the rate at which the area is changing is 0.75 cm²/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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