Maths-
General
Easy
Question
- 1
- 0
- a
none of these
none of these
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: a
![L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator sin begin display style space end style a x over denominator x cos space x end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGwAAAAjCAYAAABxaO90AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAA4JJREFUeNrtWkFkHFEYHlGrapUVUVVRonKIiF4iYlWVHCpWROghhx4it6rKLaqiKpfqIap6qaiKilBrVUWVqliVQ4mKqlghhx56iNDDilWrbP+/8408k3/mvZnd6SY77+Oz8/afN/v2/fP/73//+x3HgtGwU2AVZmGRDvQRN4g1WFLDwMK89i3iHvE3sUzsNfi9LuIj4j6xTtwmXvbdM0t8LPRdhCzV2CJORHSJDSjriTLZM1CaDuvEZ8QclPeGOCnc95V4QWnz859b+3ItKxdDYTcEy6lrnjMNBalYIY4L994kLuF6jPjJqsoFv92bmMwoCosTnLDrHfV9VxZcooePxOtwm91WVUfIEpeJO8T+BBVWgyWqVnkYcv8crHbIqkjGfawdSSnswNfOB/yeJyvCLU5b1QRHcPUEFfaTeFZpL0ApUuT6jngO1r9lXaKMWawzSSmMw/IXeDF43Volvvfd04PvVAUViK+biaq6OiyLwfyDibqYoMIYDxApLsDa9pWwPkMsES8J/dYQOUbCFeI3jXzTGmok9CQdAq+FyKdg5hYnBA+J8yGyhsJ5O13tR1AaxVRu8Z+xG7AgeqiE7Not2rBHOdTIa6cgGuxUHsNIwB5FlZfte31ywOmRVxr5ShvHV4BLruA69eAznJkQ+VPi3TaNbRTW3Q1KWfHUoaTZafPh2ssQ+WfnKOvM692HCAEKW3Y2RP7WcY8hPFxz3FxcqvErZMHjlMqA4yY3vbbksrxN9xI22aZYRoQ6EiCvOsePLarWKTYPPoibgwIk3NFEQpzvMzmvYtTtdLdmHawEWKDOwrjYZdjQws5YC2seY3CJfKobNeEZdQ3j63U75fHRiyguC7e3mECUyJFhDi8D/9a4pk+UUrI8nsnlbD+It4X1eQdumD+lKiyTcrpmxtgyZBAh9ivtPY3FxN2H7SI4umfYx6SU7KrjHu1Pwu3y/1j1JQz4/wyiPYi2f1thUk4Xd4ypgUkpWVHzAhSFjXoBblqFSTld3DGmCrpSMg5ezof0rwpBVEYIekzK6eKOMVXQlZLp1pogubSt0JXTxR1jamBSSnbQIgtTEVROF3eMqYBpKdmywRo2Ibi/Ukgfk7LuKGPseEQpJetDKD+FieYDXDVnOoyocADtIbTzmnB9o4Vj7GjEKSXj0P6L46bGtgWL8o522Gq+O3KZhEk5XTNj/Ie/w5YvcerVmacAAAFPdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPkw8L21pPjxtc3ViPjxtaT50PC9taT48bXJvdz48bWk+eDwvbWk+PG1vIHN0cmV0Y2h5PSJmYWxzZSI+JiN4MjE5Mjs8L21vPjxtbj4wPC9tbj48L21yb3c+PC9tc3ViPjxtZnJhYz48bXJvdz48bWk+c2luPC9taT48bXN0eWxlIGRpc3BsYXlzdHlsZT0idHJ1ZSI+PG1vPiYjeEEwOzwvbW8+PC9tc3R5bGU+PG1pPmE8L21pPjxtaT54PC9taT48L21yb3c+PG1yb3c+PG1pPng8L21pPjxtaT5jb3M8L21pPjxtbz4mI3hBMDs8L21vPjxtaT54PC9taT48L21yb3c+PC9tZnJhYz48L21hdGg+bbBg1gAAAABJRU5ErkJggg==)
We first try substitution:
=
= ![0 over 0](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJtJREFUeNpjYMAN+IB4GhCfhOKZUDGSwV4g9kPi+0DFSAKhQDwJi/gEII4kxaA1QOyGRdwRKkc0eAfEbFjEQWIvSTHoDx65X9Qy6AcpBr3E4TUOUr0GClAPLOJupAZ2EBDPxiI+n9ToB4H9QFwAxCxQb1YD8UFyUrYgEM+FBu43aBbhYRgFgwv8JxOPgsEERquj0epotDqiXnUEAHl3QY/fxbExAAAAYnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bW4+MDwvbW4+PG1uPjA8L21uPjwvbWZyYWM+PC9tYXRoPt4dSgEAAAAASUVORK5CYII=)
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.
( L'Hopital's Rule for zero over zero,
=
)
(d(sinax)/dx = a cos(ax) , -sin x)
On substituting, We get
= a
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
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A river is 40 metre wide. The depth d in metres at a distance x metres from a bank is given in the following table. Using simpson's rule, estimate the area of cross section of the river in square metres is
![](data:image/png;base64,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)
A river is 40 metre wide. The depth d in metres at a distance x metres from a bank is given in the following table. Using simpson's rule, estimate the area of cross section of the river in square metres is
![](data:image/png;base64,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)
maths-General
physics-
The refractive index of the material of the prism and liquid are 1.56 and 1.32 respectively. What will be the value of
for the following refraction
![](data:image/png;base64,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)
The refractive index of the material of the prism and liquid are 1.56 and 1.32 respectively. What will be the value of
for the following refraction
![](data:image/png;base64,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)
physics-General
physics-
An isosceles prism of angle 120° has a refractive index of 1.44. Two parallel monochromatic rays enter the prism parallel to each other in air as shown. The rays emerging from the opposite faces
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)
An isosceles prism of angle 120° has a refractive index of 1.44. Two parallel monochromatic rays enter the prism parallel to each other in air as shown. The rays emerging from the opposite faces
![](data:image/png;base64,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)
physics-General
physics-
If the interatomic spacing in a steel wire is
the force constant =…..
If the interatomic spacing in a steel wire is
the force constant =…..
physics-General
maths-
maths-General
maths-
In the figure rectangle ABCD, what is the probability that a randomly chosen point that in ABCD lies inside the triangle ABE is ![](data:image/png;base64,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)
In the figure rectangle ABCD, what is the probability that a randomly chosen point that in ABCD lies inside the triangle ABE is ![](data:image/png;base64,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)
maths-General
physics-
Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of the surfaces of the lenses are as given in the diagrams
Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of the surfaces of the lenses are as given in the diagrams
physics-General
physics-
Shown in the figure here is a convergent lens placed inside a cell filled with a liquid. The lens has focal length + 20 cm when in air and its material has refractive index 1.50. If the liquid has refractive index 1.60, the focal length of the system is
![](data:image/png;base64,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)
Shown in the figure here is a convergent lens placed inside a cell filled with a liquid. The lens has focal length + 20 cm when in air and its material has refractive index 1.50. If the liquid has refractive index 1.60, the focal length of the system is
![](data:image/png;base64,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)
physics-General