Find the equation of all lines having 0 slope and that are tange

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 Multiple Choice QuestionsShort Answer Type

101. Find the point on the curve y = x3 – 11 x + 5 at which the tangent has the equation y = x – 11.
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102.

Find the point on the curve y = x3 – 2x2 – 2x at which the tangent lines are parallel to the line y = 2x – 3.

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103.

Find the points on the curve y = x3 – 2x2 – x at which the tangent lines are parallel to the line y = 3x – 2.

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104.

Find the equation of the tangent to the curve x2 + 3y = 3, which is parallel to the line y – 4x + 5 = 0. 

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105.

Find the equations of all lines having slope -1 that are tangents to the curve straight y equals fraction numerator 1 over denominator straight x minus 1 end fraction. straight x not equal to 1.

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106.

Find the equation of all lines having slope 2 and being tangent to the curve straight y plus fraction numerator 2 over denominator straight x minus 3 end fraction space equals space 0.

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 Multiple Choice QuestionsLong Answer Type

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107.

Find the equation of all lines having 0 slope and that are tangent to the curve straight y equals fraction numerator 1 over denominator straight x squared minus 2 straight x plus 2 end fraction.


The equation of the curve is straight y space equals space fraction numerator 1 over denominator straight x squared minus 2 straight x plus 2 end fraction
therefore space space space space dy over dx space equals space fraction numerator left parenthesis straight x squared minus 2 straight x plus 2 right parenthesis. space 0 minus 1 left parenthesis 2 straight x minus 2 right parenthesis over denominator left parenthesis straight x squared minus 2 straight x plus 2 right parenthesis squared end fraction space equals space fraction numerator negative 2 straight x plus 2 over denominator left parenthesis straight x squared minus 2 straight x plus 2 right parenthesis squared end fraction
therefore space space space space space slope space of space tangent space space equals space fraction numerator negative 2 straight x plus 2 over denominator left parenthesis straight x squared minus 2 straight x plus 2 right parenthesis squared end fraction
But space slope space of space tangent space space equals space 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis given right parenthesis
therefore space space space space space space space fraction numerator negative 2 straight x plus 2 over denominator left parenthesis straight x squared minus 2 straight x plus 2 right parenthesis squared end fraction space equals space 0 space space space space space rightwards double arrow space space space space space minus 2 straight x plus 2 space equals space 0 space rightwards double arrow space space space space straight x space equals space 1
When space straight x space equals space 1 comma space space space straight y space equals space fraction numerator 1 over denominator 1 minus 2 plus 2 end fraction space equals space 1
therefore space space space space space point space is space left parenthesis 1 comma space 1 right parenthesis.
therefore space space space space space equation space of space tangent space left parenthesis 1 comma space 1 right parenthesis space with space slope space 0 space is
space space space space space space space space space space space space space space space space space straight y minus 1 space equals space 0 left parenthesis straight x minus 1 right parenthesis space space space space or space space space space straight y minus 1 space equals space 0

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 Multiple Choice QuestionsShort Answer Type

108.

Find the equation of the tangent to the curve straight y equals square root of 3 straight x minus 2 end root which is parallel to the line 4x - 2y + 5 = 0

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 Multiple Choice QuestionsLong Answer Type

109.

Find the equation of tangents to the curve
y = cos (x + y), – 2 straight pi ≤ x ≤ 2 straight pi
that are parallel to the line x + 2y = 0.

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110.

Find the point on curve 4x2 + 9y2 = 1, where the tangents are perpendicular to the line 2y + x = 0.

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