Question Type 2: Calculating the normal to the curve at the point where tangent is known Exercises

Question 1

Consider the curve defined by $y = \ln(x)$ .

Find the equation of the normal to the curve at $x=4$ .

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Question 2

Determine the equation of the normal to the curve $y=\arctan(x)$ at $x=1$ .

[5]

Question 3

Calculate the equation of the normal to the curve $y = e^{2x} + x$ at the point where the tangent has slope 5.

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Question 4

Consider the curve defined by the equation $y = \sin x + x$ for $0 \le x \le \pi$ .

Find the equation of the normal to the curve at the point where the tangent has a gradient of 1.

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Question 5

Find the equation of the normal to the curve $x^3+y^3=6xy$ at the point $(3,3)$ .

[6]

Question 6

Find the equation of the normal to the curve $y=\tfrac{x}{x-1}$ at $x=2$ .

[6]

Question 7

Find the equations of the normals to the curve $y = x^3 - 3x + 2$ at the points where the tangent has slope 6.

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Question 8

Find the equation of the normal to the curve defined by $x^2+xy+y^2=7$ at the point $(1,2)$ .

[6]

Question 9

Determine the equation of the normal to the curve $y = \frac{1}{x}$ at the point where $x = -1$ .

[5]

Question 10

Calculate the equation of the normal to the curve $y^2=4x+8y$ at the point $(0,0)$ .

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