# The position of an object moving along a line is given by #p(t) = 7t - cos(( pi )/3t) + 2 #. What is the speed of the object at #t = 5 #?

The speed is

We need

The derivative of position is the speed.

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To find the speed of the object at t = 5, we need to find the derivative of the position function p(t) with respect to time (t), which gives us the velocity function. Then, we evaluate the velocity function at t = 5 to determine the speed of the object.

Given: p(t) = 7t - cos((pi)/3t) + 2

To find velocity (v), we differentiate p(t) with respect to t:

v(t) = dp(t)/dt = d(7t - cos((pi)/3t) + 2)/dt

Now, we evaluate v(t) at t = 5:

v(5) = d(7(5) - cos((pi)/3(5)) + 2)/dt

After finding v(5), we get the speed of the object at t = 5.

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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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