Question

The hyperbolic tangent function tanh, where $ anh(x) = frac{e^x - e^{-x}}{e^x + e^{-x}}$, is used as an activation function for neural networks to determine the output (in the interval [-1,1]) of each neuron based on its inputs. The derivative of tanh is given by: $frac{d}{dx} anh(x) = 1 - anh^2(x)$. a) By hand, find the first three Taylor polynomials $p_0(x)$, $p_1(x)$ and $p_2(x)$ of tanh(x) about the point 0. b) Using Matlab, plot tanh(x), $p_0(x)$, $p_1(x)$ and $p_2(x)$ for the interval [-?, ?].

          The hyperbolic tangent function tanh, where
$	anh(x) = frac{e^x - e^{-x}}{e^x + e^{-x}}$,
is used as an activation function for neural networks to determine the output
(in the interval [-1,1]) of each neuron based on its inputs. The derivative of tanh
is given by:
$frac{d}{dx}	anh(x) = 1 - 	anh^2(x)$.
a) By hand, find the first three Taylor polynomials $p_0(x)$, $p_1(x)$ and $p_2(x)$ of
tanh(x) about the point 0.
b) Using Matlab, plot tanh(x), $p_0(x)$, $p_1(x)$ and $p_2(x)$ for the interval [-?, ?].

$The hyperbolic tangent function tanh, where anh(x) = frace^x - e^-xe^x + e^-x, is used as an activation function for neural networks to determine the output (in the interval [-1,1]) of each neuron based on its inputs. The derivative of tanh is given by: fracddx anh(x) = 1 - anh^2(x). a) By hand, find the first three Taylor polynomials p0(x), p1(x) and p2(x) of tanh(x) about the point 0. b) Using Matlab, plot tanh(x), p0(x), p1(x) and p2(x) for the interval [-?, ?].$

Added by John W.

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