# How do you use linear approximation to estimate #g(2.95)# and #g(3.05)# if you know that #g(3)=-5#?

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To estimate ( g(2.95) ) and ( g(3.05) ), use linear approximation:

- Find the slope of the function at ( x = 3 ) using the derivative ( g'(x) ).
- Use the point-slope form of a linear equation to find the linear approximation.
- Plug in ( x = 2.95 ) and ( x = 3.05 ) into the linear equation to estimate ( g(2.95) ) and ( g(3.05) ).

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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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- A differentiable function has the property that f(5) = 4 and f'(5) = 3. What is the estimate for f(4.8) using the local linear approximation for f at x=5?

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