Question
![3 over 2](data:image/png;base64,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)
- 0
![2 over 3](data:image/png;base64,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)
![1 third](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAKNJREFUeNpjYMAP1IC4FogvMFAIFgNxGhD/Z6ASGDVo1KBBYdB/LHgUDCbwn0w8CgYLcATibUD8DYh/APEtIJ4AxMKkGrQfiIOAmA1JzACId1DLpZ+oYYgSEN+gxABxIE6EhpMXNbJMAaVeEgTiACA+CcT21AgjHqhhVAE/qGGIHjTASQIHgTgUiFmAmAma0u8DcTypBtkC8RaoV35AU7oPPg0ArQs4erRAu/EAAABidEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xPC9tbj48bW4+MzwvbW4+PC9tZnJhYz48L21hdGg+q+QgMwAAAABJRU5ErkJggg==)
Hint:
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 fraction numerator 1 over denominator sin squared space x end fraction minus fraction numerator 1 over denominator space x squared end fraction](data:image/png;base64,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)
= ![Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x squared minus space sin squared x over denominator x squared sin squared space x end fraction space equals space Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator left parenthesis x plus space sin x right parenthesis space left parenthesis x minus space sin x right parenthesis space over denominator x squared sin squared space x end fraction space cross times x squared over x squared space equals Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator left parenthesis x plus space sin x right parenthesis space left parenthesis x minus space sin x right parenthesis space over denominator x to the power of 4 end fraction space cross times fraction numerator x squared over denominator sin squared x squared end fraction
left parenthesis space W e space k n o w space t h a t space Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator sin x space over denominator x end fraction space equals 1 right parenthesis](data:image/png;base64,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)
Also we know that sin= (
)
![space Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator left parenthesis x plus space sin x right parenthesis space left parenthesis x minus space sin x right parenthesis space over denominator x to the power of 4 end fraction space space space left parenthesis fraction numerator 0 over denominator 0 space end fraction space f o r m right parenthesis
Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator left parenthesis 2 x minus space fraction numerator x cubed over denominator 3 factorial end fraction plus fraction numerator x to the power of 5 over denominator 5 factorial end fraction....... right parenthesis space left parenthesis space fraction numerator x cubed over denominator 3 factorial end fraction minus fraction numerator x to the power of 5 over denominator 5 factorial end fraction....... right parenthesis over denominator 4 x to the power of 4 end fraction
Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator left parenthesis space fraction numerator 2 x to the power of 4 over denominator 3 factorial end fraction plus fraction numerator x to the power of 6 over denominator 5 factorial space cross times 5 factorial end fraction....... right parenthesis over denominator 4 x to the power of 4 end fraction space equals fraction numerator 2 over denominator 3 factorial space cross times 4 end fraction space equals 1 over 24 equals 1 over 12](data:image/png;base64,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Direct substitution can sometimes be used to calculate the limits for functions involving trigonometric functions.
Related Questions to study
If the excess pressure inside a soap bubble is balanced by oil column of height 2 mm then the surface tension of soap solution will be
If the excess pressure inside a soap bubble is balanced by oil column of height 2 mm then the surface tension of soap solution will be
The quadratic equation whose roots are I and m where
is
The quadratic equation whose roots are I and m where
is
Two bubbles A and B (A>B) are joined through a narrow tube than,
Two bubbles A and B (A>B) are joined through a narrow tube than,
Direct substitution can sometimes be used to calculate the limits for functions involving trigonometric functions.
Direct substitution can sometimes be used to calculate the limits for functions involving trigonometric functions.
In capillary pressure below the curved surface at water will be
In capillary pressure below the curved surface at water will be
is equal to
The substitution rule for calculating limits is a method of finding limits, by simply substituting the value of x with the point at which we want to calculate the limit.
is equal to
The substitution rule for calculating limits is a method of finding limits, by simply substituting the value of x with the point at which we want to calculate the limit.
A spherical drop of coater has radius 1 mm if surface tension of context is
difference of pressures betweca inside and outside of the spherical drop is
A spherical drop of coater has radius 1 mm if surface tension of context is
difference of pressures betweca inside and outside of the spherical drop is
The substitution rule for calculating limits is a method of finding limits, by simply substituting the value of x with the point at which we want to calculate the limit.
The substitution rule for calculating limits is a method of finding limits, by simply substituting the value of x with the point at which we want to calculate the limit.
The radii of two soap bubbles are r1 and r2. In isothermal conditions two meet together is vacum. Then the radius of the resultant bubble is given by
The radii of two soap bubbles are r1 and r2. In isothermal conditions two meet together is vacum. Then the radius of the resultant bubble is given by
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
The excess of pressure inside a soap bubble than that of the other pressure is
The excess of pressure inside a soap bubble than that of the other pressure is
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or