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What is the equation of the tangent line of #f(x)=cosx-e^x/sinx # at #x=pi/3#?

Answer 1

#y=(-sqrt(3)/2+2/3*e^(pi/3)-2e^(pi/3))/sqrt(3)x+1/2-2e^(pi/3)/sqrt(3)-1/3*(-sqrt(3)/2+2/3*e^(pi/3)-2e^(pi/3)/sqrt(3))*pi#

We get #f(pi/3)=1/2-2e^(pi/3)/sqrt(3)#

#f'(pi/3)=-sqrt(3)/2+2e^(pi/3)/3-2e^(pi/3)/sqrt(3)#

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Answer 2

Charles Arocha

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

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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.

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