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For #f(x)=(2x+1)^2/(x+1/2) # what is the equation of the tangent line at #x=-1#?

Answer 1

The equation of the tangent line at #x=−1# is #f(x)#.

#f(x)=(2x+1)^2/(x+1/2) # #f(x)=(2 (x+1/2))^2/(x+1/2) # #f(x)=4 xx (x+1/2) # #f(x)=4x +2 # : this is the equation of a straight line.

#=> f(x)# and the tangent line at #x=−1 #are coincident lines. https://tutor.hix.ai

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Answer 2

Aurora Alvarado

The equation of the tangent line at x=-1 for the function f(x)=(2x+1)^2/(x+1/2) is y = -3x - 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.