# If # A = 9/16(4r-sin(4r)) # and #(dr)/dt=0.7# when #r=pi/4# then evaluate # (dA)/dt # when #r=pi/4#?

# [ (dA)/dt ]_(r=pi/4) = 3.15 #

We have:

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To evaluate (dA)/dt when r = π/4, we first need to find the expression for dA/dt using the given information.

Given: A = (9/16)(4r - sin(4r)) (dr)/dt = 0.7 when r = π/4

To find (dA)/dt, we differentiate A with respect to t using the chain rule:

dA/dt = (9/16)(d/dt)(4r - sin(4r))

Using the chain rule and given (dr)/dt:

dA/dt = (9/16)[4(dr/dt) - cos(4r)(4(dr/dt))]

Substituting the values:

r = π/4 (dr)/dt = 0.7

We can find the value of cos(4r):

cos(4r) = cos(4(π/4)) = cos(π) = -1

Now substitute the values into the expression:

dA/dt = (9/16)[4(0.7) - (-1)(4)(0.7)]

Solve this expression to find the value of dA/dt.

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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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