Maths-
General
Easy
Question
Hint:
We can apply L'Hopital's rule, also commonly spelled L'Hospital's rule, whenever direct substitution of a limit yields an indeterminate form. This means that the limit of a quotient of functions (i.e., an algebraic fraction) is equal to the limit of their derivatives.
In this question, we have to find value of 
.
The correct answer is:
We first try substitution:
= 
Since the limit is in the form 0 over 0, it is indeterminate—we don’t yet know what is it. We need to do some work to put it in a form where we can determine the limit.
( cos2x = 1 - 2sin2x )
(
)
so, simply
=
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 
Related Questions to study
physics-
A wire of length L and radius r is rigidly fixed at one end on stretching the other end of the wire a force F the increase in its lengths is L. If another wire of same material but of length 2 L and radius 2r, is stretched with a force of 2F, the increase in its length will he
A wire of length L and radius r is rigidly fixed at one end on stretching the other end of the wire a force F the increase in its lengths is L. If another wire of same material but of length 2 L and radius 2r, is stretched with a force of 2F, the increase in its length will he
physics-General
physics-
Consider the situation shown in figure. Water 
is filled in a breaker upto a height of 10 cm. A plane mirror fixed at a height of 5 cm from the surface of water. Distance of image from the mirror after reflection from it of an object O at the bottom of the beaker is
Consider the situation shown in figure. Water is filled in a breaker upto a height of 10 cm. A plane mirror fixed at a height of 5 cm from the surface of water. Distance of image from the mirror after reflection from it of an object O at the bottom of the beaker is
physics-General
physics-
One side of a glass slab is silvered as shown. A ray of light is incident on the other side at angle of incidence 
. Refractive index of glass is given as 1.5. The deviation of the ray of light from its initial path when it comes out of the slab is
One side of a glass slab is silvered as shown. A ray of light is incident on the other side at angle of incidence . Refractive index of glass is given as 1.5. The deviation of the ray of light from its initial path when it comes out of the slab is
physics-General
physics-
A plane mirror is placed at the bottom of the tank containing a liquid of refractive index 
. P is a small object at a height h above the mirror. An observer O-vertically above P outside the liquid see P and its image in the mirror. The apparent distance between these two will be
A plane mirror is placed at the bottom of the tank containing a liquid of refractive index . P is a small object at a height h above the mirror. An observer O-vertically above P outside the liquid see P and its image in the mirror. The apparent distance between these two will be
physics-General
physics-
If an object moves towards a plane mirror with a speed v at an angle 
to the perpendicular to the plane of the mirror, find the relative velocity between the object and the image
If an object moves towards a plane mirror with a speed v at an angle to the perpendicular to the plane of the mirror, find the relative velocity between the object and the image
physics-General
physics-
Figure shows a cubical room ABCD with the wall CD as a plane mirror. Each side of the room is 3m. We place a camera at the midpoint of the wall AB. At what distance should the camera be focussed to photograph an object placed at A
Figure shows a cubical room ABCD with the wall CD as a plane mirror. Each side of the room is 3m. We place a camera at the midpoint of the wall AB. At what distance should the camera be focussed to photograph an object placed at A
physics-General
physics-
Two point white dots are 1mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which dots can be resolved by the eye ? [Take wavelength of light = 500 nm]
Two point white dots are 1mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which dots can be resolved by the eye ? [Take wavelength of light = 500 nm]
physics-General
Maths-
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 
Maths-General
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
Maths-
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 
Maths-General
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
Maths-
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 
Maths-General
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
physics-
A container is filled with water ( = 1.33) upto a height of 33.25 cm. A concave mirror is placed 15 cm above the water level and the image of an object placed at the bottom is formed 25 cm below the water level. The focal length of the mirror is
A container is filled with water ( = 1.33) upto a height of 33.25 cm. A concave mirror is placed 15 cm above the water level and the image of an object placed at the bottom is formed 25 cm below the water level. The focal length of the mirror is
physics-General
physics-
light source is located at 
as shown in the figure. All sides of the polygon are equal. The intensity of illumination at 
is 
. What will be the intensity of illumination at 
light source is located at as shown in the figure. All sides of the polygon are equal. The intensity of illumination at is . What will be the intensity of illumination at
physics-General
physics-
A container of volume 1m3 is divided into two equal compartments, one of which contains an ideal gas at 300 K The other compartment is vacuum The whole system is thermally isolated from its surroundings The partition is removed and the gas expands to occupy the whole volume of the container Its temperature now would be
A container of volume 1m3 is divided into two equal compartments, one of which contains an ideal gas at 300 K The other compartment is vacuum The whole system is thermally isolated from its surroundings The partition is removed and the gas expands to occupy the whole volume of the container Its temperature now would be
physics-General
physics-
Two moles of an ideal monoatomic gas at 
occupies a volume of V If the gas is expanded adiabatically to the volume 2V, then the work done by the gas will be
Two moles of an ideal monoatomic gas at occupies a volume of V If the gas is expanded adiabatically to the volume 2V, then the work done by the gas will be
physics-General
physics-
One mole of an ideal gas undergoes an isothermal change at temperature 'T' so that its volume V is doubled R is the molar gas constant Work done by the gas during this change is
One mole of an ideal gas undergoes an isothermal change at temperature 'T' so that its volume V is doubled R is the molar gas constant Work done by the gas during this change is
physics-General
