# If f(-2)=1 and f'(-2)=5, what is the approximate value of f(-2.01)?

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The above equation then becomes

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To approximate the value of ( f(-2.01) ), you can use the tangent line approximation formula:

[ f(x) \approx f(a) + f'(a)(x - a) ]

Given ( a = -2 ), ( f(-2) = 1 ), and ( f'(-2) = 5 ), you can plug these values into the formula:

[ f(-2.01) \approx 1 + 5(-2.01 - (-2)) ]

[ f(-2.01) \approx 1 + 5(-0.01) ]

[ f(-2.01) \approx 1 - 0.05 ]

[ f(-2.01) \approx 0.95 ]

So, the approximate value of ( f(-2.01) ) is ( 0.95 ).

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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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