Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Target Exercise 7.1>Q 4

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The tangent lines for the curve $y = \int_{0}^{x} 2 |t| d t$ which are parallel to the bisector of the first quadrant angle, is given by

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Important Questions on dy/dx as a Rate Measurer & Tangents, Normals

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IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Target Exercise 7.1>Q 5

The equation of normal to

x + y = x^{y}

, where it intersects

x

-axis, is given by:

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Target Exercise 7.1>Q 6

The equation of normal at any point

θ

to the curve

x = a \cos θ + a θ \sin θ, y = a \sin θ - a θ \cos θ

,

a > 0

is always at a distance of

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Target Exercise 7.1>Q 7

If the tangent at

(x_{0}, y_{0})

to the curve

x^{3} + y^{3} = a^{3}

meets the curve again at

(x_{1}, y_{1})

then

\frac{x_{1}}{x_{0}} + \frac{y_{1}}{y_{0}}

is equal to

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Target Exercise 7.1>Q 8

The area bounded by the axes of reference and the normal to

y = \log_{e} x

at

(1, 0)

, is

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Target Exercise 7.1>Q 9

If

\frac{x}{a} + \frac{y}{b} = 2

touches the curve

\frac{x^{n}}{a^{n}} + \frac{y^{n}}{b^{n}} = 2

at the point

(α, β)

and

n, a, b \neq 0

, then

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Target Exercise 7.1>Q 10

The equation of tangents to the curve

y = \cos (x + y), - 2 π \leq x \leq 2 π

that are parallel to the line

x + 2 y = 0

, is:

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Target Exercise 7.2>Q 1

The angle of intersection of

y = a^{x}

and

y = b^{x}

, is given by:

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Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Target Exercise 7.2>Q 2

The angle between the curves

x^{2} + 4 y^{2} = 32

and

x^{2} - y^{2} = 12

, is: