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What is the equation of the tangent line of # f(x)=sinpix # at # x=3 #?

Answer 1

Charles Anctil

#y = pi(3-x)#

#color(blue)("Graph of "f(x))# graph{sin(pix) [-10, 10, -5, 5]}

Either two points are required to construct a straight line, or one would prefer to use a point and the gradient.

#f(3) = 0#

We know that the line passes through the point #(3,0)#.

#f'(x) = picospix#

#f'(3) = -pi#

We know that the gradient of the line is #-pi#.

#-pi = frac{y-0}{x-3}#

the tangent line equation:

#y = pi(3-x)#

#color(blue)("Graph of tangent line")# graph{pi(3-x) [-10, 10, -5, 5]}

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Answer 2

Charles Arocha

The equation of the tangent line of f(x)=sinpix at x=3 is y = -picos(3pi)(x-3) + sin(3pi).

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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.