Let S be a square with side of length x If we approximate the change in size of the area of S by hdAdxxx0 when the sides are changed from x0 to x0h then the absolute value of the error in our approximation is

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Proficiency in 'dy/dx as a Rate Measurer & Tangents, Normals' Exercise 1>Q 30

Consider

f (x) = \int_{1}^{x} (t + \frac{1}{t}) d t

and

g (x) = f^{'} (x)

for

x \in [\frac{1}{2}, 3]

. If

P

is a point on the curve

y = g (x)

such that the tangent to this curve at

P

is parallel to a chord joining the points

(\frac{1}{2}, g (\frac{1}{2}))

and

(3, g (3))

of the curve, then the coordinates of
the point

P

:

EASY

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Proficiency in 'dy/dx as a Rate Measurer & Tangents, Normals' Exercise 1>Q 31

If

f

is an odd continuous function in

[- 1, 1]

and differentiable in

(- 1, 1)

, then:

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Proficiency in 'dy/dx as a Rate Measurer & Tangents, Normals' Exercise 1>Q 32

The parabola $y = x^{2} + p x + q$ intercepts the straight line $y = 2 x - 3$ at a point with abscissa $1 .$ If the distance between the vertex of the parabola and the $x -$ axis is least, then:

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Proficiency in 'dy/dx as a Rate Measurer & Tangents, Normals' Exercise 1>Q 33

The abscissa of the point on the curve

\sqrt{x y} = a + x

, the tangent at which cuts off equal intercepts from the coordinate axes is

(a > 0)

:

EASY

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Proficiency in 'dy/dx as a Rate Measurer & Tangents, Normals' Exercise 1>Q 34

If the side of a triangle vary slightly $(d a, d b, d c)$ in such a way that its circumradius remains constant, then $\frac{d a}{\cos A} + \frac{d b}{\cos B} + \frac{d c}{\cos C}$ is equal to

MEDIUM

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Proficiency in 'dy/dx as a Rate Measurer & Tangents, Normals' Exercise 1>Q 35

Let

f (x)

satisfy the requirements of Lagrange’s mean value theorem in

[0, 1]

,

f (0) = 0

and

f^{'} (x) \leq 1 - x, \forall x \in (0, 1)

, then:

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Proficiency in 'dy/dx as a Rate Measurer & Tangents, Normals' Exercise 1>Q 36

For function

f (x) = \frac{l n x}{x}

, which of the following statements are true?

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Proficiency in 'dy/dx as a Rate Measurer & Tangents, Normals' Exercise 1>Q 37

Equation of a line which is tangent to both the curves

y = x^{2} + 1

and

y = - x^{2}

is

Let $S$ be a square with side of length $x$ . If we approximate the change in size of the area of $S$ by $h$ . ${\frac{d A}{d x}|}_{x = x_{0}}$ , when the sides are changed from $x_{0}$ to $x_{0} + h$ , then the absolute value of the error in our approximation, is:

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

Learn and Prepare for any exam you want !

Let S be a square with side of length x. If we approximate the change in size of the area of S by h. dAdxx=x0, when the sides are changed from x0 to x0+h, then the absolute value of the error in our approximation, is:

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

Learn and Prepare for any exam you want !

Let $S$ be a square with side of length $x$ . If we approximate the change in size of the area of $S$ by $h$ . ${\frac{d A}{d x}|}_{x = x_{0}}$ , when the sides are changed from $x_{0}$ to $x_{0} + h$ , then the absolute value of the error in our approximation, is: