How do you find the linearization of #f(x) = e^(5 x)# at the point x=0?

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Answer 1 · 2016-12-29T23:14:08

#e^(5x) ~= 1+5x#

The linearization of #f(x)# is its approximation using the tangent line:

#y(x) = f(x_0) + f'(x_0)(x-x_0)#

in our case:

#f(x) = e^(5x)#
#f'(x) = 5e^(5x)#

So for #x_0=0#

#f(0) = 1#
#f'(0) = 5#

and the approximation is:

#e^(5x) ~= 1+5x#