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

Answer 1

Ezekiel Alexander

#y=-5x+6#

#•color(white)(x)m_(color(red)"tangent")=f'(x)" at x = a"#

#"differentiate using the "color(blue)"quotient rule"#

#"given "f(x)=(g(x))/(h(x))" then"#

#f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2#

#g(x)=-x^2-x+3rArrg'(x)=-2x-1#

#h(x)=2x-1rArrh'(x)=2#

#rArrf'(x)=((2x-1)(-2x-1)-2(-x^2-x+3))/(2x-1)^2#

#rArrf'(1)=(-3-2)/1=-5#

#rArrf(1)=1to(1,1)larr" tangent point"#

#rArry-1=-5(x-1)#

#rArry=-5x+6larr" equation of tangent"#

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Answer 2

Luke Alvarez

The equation of the tangent line of f(x) = (-x^2-x+3)/(2x-1) at x=1 is y = -2x + 5.

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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.