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$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x 10 to the power of x minus x over denominator 1 minus cos space x end fraction equals$

log 10
3log 10
2log 10
4log 10

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 $L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x 10 to the power of x minus x over denominator 1 minus cos space x end fraction$ .

The correct answer is: 2log 10

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x 10 to the power of x minus x over denominator 1 minus cos space x end fraction$
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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 $fraction numerator plus-or-minus infinity over denominator plus-or-minus infinity end fraction.$

$L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator n open parentheses 1 cubed plus 2 cubed plus midline horizontal ellipsis times plus n cubed close parentheses squared over denominator open parentheses 1 squared plus 2 squared plus midline horizontal ellipsis plus n squared close parentheses cubed end fraction equals$

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A capillary tube at radius R is immersed in water and water rises in it to a height H. Mass of water in the capillary tube is M. If the radius of the tube is doubled. Mass of water that will rise in the, capillary tube will now be

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$Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 1 over denominator sin squared space x end fraction minus fraction numerator 1 over denominator sinh squared space x end fraction equals$

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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 $C r equals 1 space a n d space d e n s i t y space d equals 0.8 g m divided by c c right parenthesis$

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The quadratic equation whose roots are I and m where $l equals lim for theta not stretchy rightwards arrow 0 of open parentheses fraction numerator 3 sin space theta minus 4 sin cubed space theta over denominator theta end fraction close parentheses m equals lim for theta not stretchy rightwards arrow 0 of open parentheses fraction numerator 2 tan space theta over denominator theta open parentheses 1 minus tan squared space theta close parentheses end fraction close parentheses$ is

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Two bubbles A and B (A>B) are joined through a narrow tube than,

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$L subscript x not stretchy rightwards arrow 0 end subscript equals fraction numerator tan cubed begin display style space end style x minus sin cubed space x over denominator x cubed end fraction$

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In capillary pressure below the curved surface at water will be

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$L subscript x not stretchy rightwards arrow 0 end subscript equals fraction numerator sin begin display style space end style open parentheses pi cos squared space x close parentheses over denominator x squared end fraction$ is equal to

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A spherical drop of coater has radius 1 mm if surface tension of context is $70 cross times 10 to the power of negative 3 end exponent straight N divided by straight m$ difference of pressures betweca inside and outside of the spherical drop is

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$L t subscript x plus 0 end subscript fraction numerator left parenthesis 1 minus cos space 2 x right parenthesis left parenthesis 3 plus cos space x right parenthesis over denominator x tan space 4 x end fraction text is equal to end text$

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$Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator tan begin display style space end style x minus sin space x over denominator x squared end fraction equals$

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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

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$Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator x over denominator square root of x plus 4 end root minus 2 end fraction equals$

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The excess of pressure inside a soap bubble than that of the other pressure is

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Related Questions to study

A capillary tube at radius R is immersed in water and water rises in it to a height H. Mass of water in the capillary tube is M. If the radius of the tube is doubled. Mass of water that will rise in the, capillary tube will now be

A capillary tube at radius R is immersed in water and water rises in it to a height H. Mass of water in the capillary tube is M. If the radius of the tube is doubled. Mass of water that will rise in the, capillary tube will now 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

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

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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,

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In capillary pressure below the curved surface at water will be

is equal to

is equal to

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 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

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log 10
3log 10
2log 10
4log 10

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 $C r equals 1 space a n d space d e n s i t y space d equals 0.8 g m divided by c c right parenthesis$

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 $C r equals 1 space a n d space d e n s i t y space d equals 0.8 g m divided by c c right parenthesis$

$L subscript x not stretchy rightwards arrow 0 end subscript equals fraction numerator sin begin display style space end style open parentheses pi cos squared space x close parentheses over denominator x squared end fraction$ is equal to

$L subscript x not stretchy rightwards arrow 0 end subscript equals fraction numerator sin begin display style space end style open parentheses pi cos squared space x close parentheses over denominator x squared end fraction$ is equal to

A spherical drop of coater has radius 1 mm if surface tension of context is $70 cross times 10 to the power of negative 3 end exponent straight N divided by straight m$ 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 $70 cross times 10 to the power of negative 3 end exponent straight N divided by straight m$ difference of pressures betweca inside and outside of the spherical drop is

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