# The position of an object moving along a line is given by #p(t) = 4t - tsin(( pi )/8t) #. What is the speed of the object at #t = 7 #?

I tried this (but check my maths):

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To find the speed of the object at ( t = 7 ), we need to differentiate the position function ( p(t) ) with respect to time to get the velocity function, and then evaluate it at ( t = 7 ).

The velocity function ( v(t) ) is the derivative of ( p(t) ) with respect to ( t ):

[ v(t) = \frac{dp}{dt} ]

Let's find the derivative of ( p(t) ) with respect to ( t ):

[ p(t) = 4t - t\sin\left(\frac{\pi}{8t}\right) ]

[ \frac{dp}{dt} = 4 - \left(\sin\left(\frac{\pi}{8t}\right) - \frac{\pi\cos\left(\frac{\pi}{8t}\right)}{8t^2}\right) ]

Now, we evaluate ( v(t) ) at ( t = 7 ):

[ v(7) = 4 - \left(\sin\left(\frac{\pi}{56}\right) - \frac{\pi\cos\left(\frac{\pi}{56}\right)}{392}\right) ]

Now, we can calculate the numerical value of ( v(7) ) to find the speed of the object at ( t = 7 ).

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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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