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What is the equation of the tangent line of #f(x)=sqrt(1/(x^2-3x+2) # at #x=0#?

Answer 1

Emma Aldridge

#y = 3 / 2^(5/2)x + 1/2^(1/2)#

#p(x) = x^2 - 3x + 2 => f = p^(-1/2)#

#f'(x) = -1/2 p^(-3/2) (2x - 3)#

#f'(0) = -1/2 2^(-3/2) (-3) = + 3 * 2^(-5/2) = a#

The desired line is #g(x) = ax + b#

#g(0) = f(0) = sqrt{1/2} = b#

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Answer 2

Scarlett Allison

The equation of the tangent line of f(x) = sqrt(1/(x^2-3x+2)) at x=0 is y = -1.

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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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