# How do you use the tangent line approximation to approximate the value of #ln(1.006)# ?

Let us look at some details.

Hence,

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To approximate the value of ln(1.006) using the tangent line approximation, you would first find a point near 1.006 where you know the natural logarithm. Let's choose 1 as it's easy to calculate. Then, you would calculate the derivative of ln(x) at x = 1, which is simply 1.

The tangent line approximation formula is:

f(x) ≈ f(a) + f'(a)(x - a)

Plugging in the values: f(1.006) ≈ ln(1) + 1(1.006 - 1)

Simplify and calculate: f(1.006) ≈ 0 + 1(0.006) f(1.006) ≈ 0.006

So, the approximation of ln(1.006) using the tangent line at x = 1 is approximately 0.006.

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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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