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What is the equation of the tangent line of #f(x)=cos^3x/x^2 # at #x=pi/3#?

Answer 1

Christopher Allers

#y=-27(sqrt(3)pi+2)/(8*pi^3)*x+(9*cos(pi/3)^3)/pi^2+9*(sqrt(3)pi+2)/(8*pi^2)#

We get #f(pi/3)=(9cos(pi/3)^3)/pi^2# #f'(x)=-cos(x)^2(3sin(x)*x+2cos(x))/x^3#

#f'(pi/3)=-27*(sqrt(3)pi+2)/(8*pi^3)# This is the slope of the tangent line and the point #P(pi/3;(9cos(pi/3)^3)/pi^2)#

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Answer 2

William Abdalla

The equation of the tangent line of f(x)=cos^3x/x^2 at x=pi/3 is y = -3√3x + 3√3π/4 + 1/4.

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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.