What is the equation of the line tangent to #f(x)=sin x + sin^2 x # at #x=0#?

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Answer 1 · 2018-03-13T12:19:20

The equation of tangent is #y=x#

#f(x)=sinx+sin^2x ; x=0#

#:. f(0)=sin0+sin^2(0)= 0 #

Point in the curve is #(0,0)#

#f(x)=sinx+sin^2x #

#f'(x)= cosx+ 2sinxcosx #

#f'(0)= cos 0+ 2sin0cos0 #

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

Slope at the point #(0,0)# is #1#

The equation of tangent at the point is #(y-0)=1(x-0)# or

#y=x # .Therefore the equation of tangent is #y=x# [Ans]