# How do you estimate delta f using Linear Approximation and use a calculator to compute both the error and the percentage error given #f(x)=cos(x)# a=pi/4 and delta x=0.06?

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The linear approximation is:

So the estimate is:

In actual fact:

To finish this off, as I'm sure you know:

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To estimate Δf using Linear Approximation, use the formula: Δf ≈ f'(a) * Δx. For f(x) = cos(x), a = π/4, and Δx = 0.06, the first derivative is f'(x) = -sin(x). Therefore, f'(a) = -sin(π/4) = -√2/2. Thus, Δf ≈ (-√2/2) * 0.06. Compute Δf. To compute the error, find the absolute difference between the actual change in f and the estimated change in f: |Δf - f(π/4 + 0.06)|. For percentage error, divide the absolute error by the actual change in f and multiply by 100.

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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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