Question
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: ![fraction numerator negative 1 over denominator 10 end fraction](data:image/png;base64,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)
![Lt subscript x not stretchy rightwards arrow 1 end subscript space fraction numerator left parenthesis 2 x minus 3 right parenthesis left parenthesis square root of x minus 1 right parenthesis over denominator 2 x squared plus x minus 3 end fraction](data:image/png;base64,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)
has indeterminate form
, but we can factor and reduce.
![F a c t o r s space o f space 2 x squared plus x minus 3 space equals space left parenthesis 2 x plus 3 right parenthesis left parenthesis x minus 1 right parenthesis space o r space left parenthesis 2 x plus 3 right parenthesis left parenthesis square root of x plus 1 right parenthesis left parenthesis square root of x minus 1 right parenthesis](data:image/png;base64,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)
![Lt subscript x not stretchy rightwards arrow 1 end subscript space fraction numerator left parenthesis 2 x minus 3 right parenthesis left parenthesis square root of x minus 1 right parenthesis over denominator left parenthesis 2 x plus 3 space right parenthesis left parenthesis x minus 1 right parenthesis end fraction space equals space Lt subscript x not stretchy rightwards arrow 1 end subscript space fraction numerator left parenthesis 2 x minus 3 right parenthesis over denominator left parenthesis 2 x plus 3 space right parenthesis left parenthesis square root of x plus 1 right parenthesis end fraction](data:image/png;base64,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)
On substituting, We get
![fraction numerator left parenthesis 2 minus 3 right parenthesis over denominator left parenthesis 2 plus 3 space right parenthesis left parenthesis square root of 1 plus 1 right parenthesis end fraction space equals space fraction numerator negative 1 over denominator 10 end fraction](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
Related Questions to study
Assertion : A random variable X takes the values 0,1,2. It’s mean is 0.6. If P(X=0) =0.5 then P(X=1) = 0.4
Reason: If X : S
R is a discrete random variable with range
1 2 3 x , x , x ,.... then mean ![equals stretchy sum from r equals 1 to infinity of x subscript r end subscript P open parentheses X equals x subscript r end subscript close parentheses](data:image/png;base64,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)
Assertion : A random variable X takes the values 0,1,2. It’s mean is 0.6. If P(X=0) =0.5 then P(X=1) = 0.4
Reason: If X : S
R is a discrete random variable with range
1 2 3 x , x , x ,.... then mean ![equals stretchy sum from r equals 1 to infinity of x subscript r end subscript P open parentheses X equals x subscript r end subscript close parentheses](data:image/png;base64,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)
Infinite limits in calculus occur when the function is unbounded and tends toward infinity or negative infinity as x approaches a given value.
Infinite limits in calculus occur when the function is unbounded and tends toward infinity or negative infinity as x approaches a given value.
A wire of length 50 cm and cross - sectional area of 1 mm2 is extended by 1 mm what will be the required work?![open parentheses straight Y equals 2 cross times 10 to the power of 11 Nm to the power of negative 2 end exponent close parentheses](data:image/png;base64,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)
A wire of length 50 cm and cross - sectional area of 1 mm2 is extended by 1 mm what will be the required work?![open parentheses straight Y equals 2 cross times 10 to the power of 11 Nm to the power of negative 2 end exponent close parentheses](data:image/png;base64,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)
The work per unit volume to stretch the length by 1% of a wire with cross - section area 1 mm2 will be.....
The work per unit volume to stretch the length by 1% of a wire with cross - section area 1 mm2 will be.....
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
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
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
Young's modulus of the material of a wire is Y. On pulling the wire by a force F the increase in its length is x, what is the potential energy of the stretched wire?
Young's modulus of the material of a wire is Y. On pulling the wire by a force F the increase in its length is x, what is the potential energy of the stretched wire?
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