# The temperature T in #""^oC# of a particular city during a 24 hour period can be modelled by #T = 10 + 8 sin 12 pi t# where t is the time in hours, with t = 0 corresponding to midday. Find the rate at which the temperature is changing at 4pm.?

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To find the rate at which the temperature is changing at 4 pm, we need to calculate the derivative of the temperature function T with respect to time t, and then evaluate it at t = 4.

Given T = 10 + 8 sin(12πt), we first find the derivative of T with respect to t: dT/dt = 8(12π)cos(12πt)

Now, we evaluate this derivative at t = 4: dT/dt = 8(12π)cos(12π*4)

dT/dt = 8(12π)cos(48π)

dT/dt ≈ 8(12π)(1) [since cos(48π) = 1]

dT/dt ≈ 96π

Therefore, the rate at which the temperature is changing at 4 pm is approximately 96π degrees Celsius per hour.

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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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