How do you find the linearization at a=1 of #f(x) = ln(x)#?
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To find the linearization of ( f(x) = \ln(x) ) at ( a = 1 ), follow these steps:

Calculate the derivative of ( f(x) = \ln(x) ) using the differentiation rule for natural logarithm. ( f'(x) = \frac{1}{x} )

Evaluate the derivative at ( x = 1 ) to find the slope of the tangent line at ( x = 1 ). ( f'(1) = \frac{1}{1} = 1 )

Use the pointslope form of a line to write the equation of the tangent line. ( y  y_1 = m(x  x_1) )

Substitute the slope ( m ) and the point ( (x_1, y_1) = (1, \ln(1)) ) into the equation. ( y  \ln(1) = 1(x  1) )

Simplify the equation. ( y  0 = x  1 )

The linearization of ( f(x) = \ln(x) ) at ( a = 1 ) is given by: ( L(x) = x  1 )
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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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