Please help me find L ??

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Answer 1 · 2018-02-19T00:19:53

#y = -6x+3+6pi#

The linearization of a function is its tangent, and the equation of the tangent line fo the graph of #f(x)# in #x=pi# is:

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

The derivative of #f(x)# is:

#f'(x) = d/dx (3e^(2sinx)) = 6cosxe^(2sinx)#

so:

#f(pi) = 3e^(2sinpi) = 3#

#f'(pi) = 6cospi e^(2sinpi) = -6#

and the tangent is:

#y=3-6(x-pi)#

or:

#y = -6x+3+6pi#

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