How do you find the linearization of #f(x)=lnx # at x=8?
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To find the linearization of ( f(x) = \ln(x) ) at ( x = 8 ), follow these steps:

Calculate the first derivative of ( f(x) ) with respect to ( x ), denoted as ( f'(x) ). [ f'(x) = \frac{1}{x} ]

Evaluate ( f'(x) ) at ( x = 8 ). [ f'(8) = \frac{1}{8} ]

Find the value of ( f(8) ), which is simply ( \ln(8) ).

Use the pointslope form of a linear equation to construct the linearization: [ L(x) = f(a) + f'(a)(x  a) ] where ( a ) is the point of tangency, in this case, ( a = 8 ).

Substitute the values of ( f(a) ), ( f'(a) ), and ( a ) into the equation to get the linearization. Thus, the linearization of ( f(x) = \ln(x) ) at ( x = 8 ) is: [ L(x) = \ln(8) + \frac{1}{8}(x  8) ]
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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