Question
- 1
![1 half](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJFJREFUeNpjYMAP1IC4FogvMFAIFgNxGhD/Z6ASGDVo1KBBYdB/LHgUDCbwn0w8CgYLsAbiNUD8CYh/QaujaHIMOgjEkUDMA+VrAfFRqBjFQB6IL1HLyz+oYYgl1HsUAQ4gPgmNBLKBIBBvAGI3SgxRghqiQokhGkA8G4i5KDFEHIhXATELpYG7BeoimhZyWAEAI3M1I31CbrEAAABidEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xPC9tbj48bW4+MjwvbW4+PC9tZnJhYz48L21hdGg+ND6jrQAAAABJRU5ErkJggg==)
![2 over 3](data:image/png;base64,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)
![3 over 2](data:image/png;base64,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)
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: ![2 over 3](data:image/png;base64,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)
![Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator cube root of 1 plus x end root minus cube root of 1 minus x end root over denominator x end fraction](data:image/png;base64,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)
We first try substitution:
![Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator cube root of 1 plus x end root minus cube root of 1 minus x end root over denominator x end fraction equals Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator cube root of 1 plus 0 end root minus cube root of 1 minus 0 end root over denominator 0 end fraction space equals 0 over 0 space
S i n c e space t h e space l i m i t space i s space i n space t h e space f o r m space space 0 space o v e r space 0 space comma space i t space i s space i n d e t e r m i n a t e space w e space d o n ’ t space y e t space k n o w space w h a t space i s space i t. space W e space n e e d space t o space d o space s o m e space w o r k space t o space p u t space i t space i n space a space f o r m space
w h e r e space w e space c a n space d e t e r m i n e space t h e space l i m i t.
Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator cube root of 1 plus x end root minus cube root of 1 minus x end root over denominator x end fraction space equals Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator 1 over denominator 3 left parenthesis 1 plus x right parenthesis begin display style bevelled fraction numerator 2 over denominator 3 space end fraction end style cross times space left parenthesis 1 minus x right parenthesis bevelled 2 over 3 end fraction space left parenthesis u sin g space L apostrophe H o p i t a l apostrophe s space r u l e right parenthesis
p u t space x equals 0
Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator 1 over denominator 3 left parenthesis 1 plus x right parenthesis to the power of begin display style bevelled 2 over 3 end style end exponent cross times space left parenthesis 1 minus x right parenthesis to the power of begin display style bevelled 2 over 3 end style to the power of blank end exponent end fraction space equals space 1 third](data:image/png;base64,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)
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
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
The graph shown was obtained from experimental measurements of the period of oscillations T for different masses M placed in the scale pan on the lower end of the passing through the origin is that the,....
![](data:image/png;base64,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)
The graph shown was obtained from experimental measurements of the period of oscillations T for different masses M placed in the scale pan on the lower end of the passing through the origin is that the,....
![](data:image/png;base64,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)
What is the possible value of poison’s ratio?
What is the possible value of poison’s ratio?
What is the relationship between Young's modulus Y, Bulk modulus k and modulus of rigidity
?
What is the relationship between Young's modulus Y, Bulk modulus k and modulus of rigidity
?
The area of the parallelogram whose adjacent sides are
is
sq. units. If
then ![stack b with minus on top equals](data:image/png;base64,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)
The area of the parallelogram whose adjacent sides are
is
sq. units. If
then ![stack b with minus on top equals](data:image/png;base64,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)
Shearing stress causes change in
Shearing stress causes change in
A 2m long rod of radius 1cm which is fixed from one end is given a twist of 0.8 radian. The shear strain developed will be
A 2m long rod of radius 1cm which is fixed from one end is given a twist of 0.8 radian. The shear strain developed will be
Mark the wrong statement.
Mark the wrong statement.
The upper end of a wire of radius 4 mm and length 100 cm is clamped and its other end is twisted through an angle of 30° Then what is the angle of shear?
The upper end of a wire of radius 4 mm and length 100 cm is clamped and its other end is twisted through an angle of 30° Then what is the angle of shear?
The pairs
each determines a plane. Then the planes are parallel if
Cross product of two vectors is equal to the product of their magnitudes and sin of the angle between them. When two vectors are parallel, the angle between them is zero resulting their dot product as zero.
The pairs
each determines a plane. Then the planes are parallel if
Cross product of two vectors is equal to the product of their magnitudes and sin of the angle between them. When two vectors are parallel, the angle between them is zero resulting their dot product as zero.
The lower surface of a cube is fixed. On its upper surface is applied at an angle 30º of from its surface. What will be the change of the type?
The lower surface of a cube is fixed. On its upper surface is applied at an angle 30º of from its surface. What will be the change of the type?