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Find the equation of the tangent line to the graph of #y = sin2(πx3/6)# at the point with #x = 1#?

Answer 1

Luke Alvarez

Equation of tangent at #x=1)# is #y= -pi(x-1) #

#y=sin 2(pi x 3/6)=sin (pi x ) #. At # x=1#

#y(1)= sin pi =0 :.# The point is #(1,0)#

#y=sin(pi x):.# Derivative #y'= pi cos( pi x)#

At #x=1# the slope is #m=y'= pi cos (pi) = -pi#

So equation of tangent at point #(1,0)# in point slope form is

#y-0= m(x-1) or y= -pi(x-1) #

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Answer 2

Emily Ammerman

The equation of the tangent line to the graph of y = sin^2(πx^3/6) at the point with x = 1 is y = -π^2/2x + π^2/2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.