Question
- log x
- 1
![x cubed](data:image/png;base64,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)
- 0
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: 1
![L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator log subscript e begin display style space end style open parentheses 1 plus x cubed close parentheses over denominator sin cubed begin display style space end style x end fraction](data:image/png;base64,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)
![L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator log subscript e begin display style space end style open parentheses 1 plus x cubed close parentheses over denominator sin cubed begin display style space end style x end fraction space cross times x cubed over x cubed](data:image/png;base64,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)
(
= 1,
)
On substituting value, We get
= 1 x 1 = 1
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
Related Questions to study
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
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
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)
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
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)
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 ![P subscript 3 end subscript](data:image/png;base64,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)
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)
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 ![P subscript 3 end subscript](data:image/png;base64,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)
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)
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
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![left parenthesis gamma equals 5 divided by 3 right parenthesis](data:image/png;base64,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)
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![left parenthesis gamma equals 5 divided by 3 right parenthesis](data:image/png;base64,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)
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
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
If
then xy+1=
If
then xy+1=
A wire of length 2 m is made from 10 cm3 of copper. A force F is applied so that its length increases by 2 mm. Another wire of length 8 m is made from the same volume of copper. If the force F is applied to it, its length will increase by….
A wire of length 2 m is made from 10 cm3 of copper. A force F is applied so that its length increases by 2 mm. Another wire of length 8 m is made from the same volume of copper. If the force F is applied to it, its length will increase by….
The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign.
The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign.