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Linear Approximation...?
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Linear Approximation. Ah how I love thee. Until you went and got all confusing on my in 3D.
\[\color{red}{{\text{Construct a linear approximation of }}y = \tanh \left( x \right){\text{ near c}} = \ln \left( 2 \right) \approx 0.693}\]\[\color{red}{{\text{ and use \it too approximate the value of}}\tanh (0.7)}\]
L(x) = f(a) + f'(a)(x-a)
Is a 0.7 or ln(2) or 0.693?
a = c in this case
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