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General

Easy

Question

$L t left parenthesis x rightwards arrow infinity right parenthesis left parenthesis left parenthesis x plus a right parenthesis divided by left parenthesis x plus b right parenthesis right parenthesis to the power of left parenthesis x plus b right parenthesis equals$

$e (e - b)$
$e (a + b)$
$e^{a} t$

hint Hint:

In this question we are getting $1 to the power of infinity$ form and we will us standard formula $limit as x rightwards arrow infinity of open parentheses f left parenthesis x right parenthesis close parentheses to the power of g left parenthesis x right parenthesis end exponent space space equals space e to the power of limit as x rightwards arrow infinity of left parenthesis f left parenthesis x right parenthesis minus 1 right parenthesis cross times g left parenthesis x right parenthesis end exponent$ to find the limit.

The correct answer is: $e to the power of a t$

In this question we have to find the limit $limit as x minus greater than infinity of open parentheses fraction numerator x plus a over denominator x plus b end fraction close parentheses to the power of x plus b end exponent$
Step1: Putting the value of the limit
By the value the value of the limit we are getting $1 to the power of infinity$ form.
Step2: Using Standard limits
We know that $limit as x rightwards arrow infinity of open parentheses f left parenthesis x right parenthesis close parentheses to the power of g left parenthesis x right parenthesis end exponent space space equals space e to the power of limit as x rightwards arrow infinity of left parenthesis f left parenthesis x right parenthesis minus 1 right parenthesis cross times g left parenthesis x right parenthesis end exponent$
=> $e to the power of limit as x minus greater than infinity of open parentheses fraction numerator x plus a over denominator x plus b end fraction close parentheses to the power of x plus b end exponent end exponent$
=> $e to the power of limit as x minus greater than infinity of open parentheses fraction numerator x plus a over denominator x plus b end fraction minus 1 close parentheses left parenthesis x plus b right parenthesis end exponent$
=> $e to the power of limit as x minus greater than infinity of open parentheses fraction numerator x plus a minus x minus b over denominator x plus b end fraction close parentheses left parenthesis x plus b right parenthesis end exponent$
=> $e to the power of limit as x minus greater than infinity of left parenthesis a minus b right parenthesis end exponent$
=> $e to the power of a minus b end exponent$
Hence, the value of the limit is $e to the power of a minus b end exponent$

Related Questions to study

$L t subscript left parenthesis x rightwards arrow 0 right parenthesis left parenthesis e to the power of x minus e to the power of left parenthesis i n invisible function application x right parenthesis right parenthesis divided by left parenthesis 2 left parenthesis x minus s i n invisible function application x right parenthesis right parenthesis equals$

$L t subscript left parenthesis x rightwards arrow 0 right parenthesis left parenthesis e to the power of x minus e to the power of left parenthesis i n invisible function application x right parenthesis right parenthesis divided by left parenthesis 2 left parenthesis x minus s i n invisible function application x right parenthesis right parenthesis equals$

$L t subscript left parenthesis x rightwards arrow 0 right parenthesis left parenthesis left parenthesis 1 minus e to the power of x right parenthesis s i n invisible function application x right parenthesis divided by left parenthesis x squared plus x cubed right parenthesis equals$

$L t subscript left parenthesis x rightwards arrow 0 right parenthesis left parenthesis left parenthesis 1 minus e to the power of x right parenthesis s i n invisible function application x right parenthesis divided by left parenthesis x squared plus x cubed right parenthesis equals$

If $a greater than 0 text and end text Lt invisible function application left parenthesis x not stretchy rightwards arrow a right parenthesis open parentheses a to the power of x minus x to the power of 4 close parentheses divided by open parentheses x to the power of x minus a cubed close parentheses equals negative 1 text , then end text a equals$

If $a greater than 0 text and end text Lt invisible function application left parenthesis x not stretchy rightwards arrow a right parenthesis open parentheses a to the power of x minus x to the power of 4 close parentheses divided by open parentheses x to the power of x minus a cubed close parentheses equals negative 1 text , then end text a equals$

parallel

If $stack a with minus on top equals left parenthesis 3 comma negative 1 , 5 right parenthesis comma stack b with minus on top equals left parenthesis 1 , 2 comma negative 3 right parenthesis$ are given vectors. A vector $stack c with minus on top$ which is perpendicular to $z$ -axis satisfying $stack c with minus on top times stack a with minus on top equals 9$ and $stack c with minus on top times stack b with minus on top equals negative 4$ then

If $stack a with minus on top equals left parenthesis 3 comma negative 1 , 5 right parenthesis comma stack b with minus on top equals left parenthesis 1 , 2 comma negative 3 right parenthesis$ are given vectors. A vector $stack c with minus on top$ which is perpendicular to $z$ -axis satisfying $stack c with minus on top times stack a with minus on top equals 9$ and $stack c with minus on top times stack b with minus on top equals negative 4$ then

$a with minus on top equals left parenthesis c o s invisible function application theta right parenthesis times i with minus on top minus left parenthesis s i n invisible function application theta right parenthesis j with minus on top comma b with minus on top equals left parenthesis s i n invisible function application theta right parenthesis times i with minus on top plus left parenthesis c o s invisible function application theta right parenthesis j with minus on top comma c with minus on top equals k with minus on top comma r with minus on top equals 17 i with minus on top plus 7 j with minus on top plus 15 k with minus on top$ and $stack r with ‾ on top equals x stack a with ‾ on top plus y stack b with ‾ on top plus z stack c with ‾ on top$ . The range of $x plus y plus z$ is

$a with minus on top equals left parenthesis c o s invisible function application theta right parenthesis times i with minus on top minus left parenthesis s i n invisible function application theta right parenthesis j with minus on top comma b with minus on top equals left parenthesis s i n invisible function application theta right parenthesis times i with minus on top plus left parenthesis c o s invisible function application theta right parenthesis j with minus on top comma c with minus on top equals k with minus on top comma r with minus on top equals 17 i with minus on top plus 7 j with minus on top plus 15 k with minus on top$ and $stack r with ‾ on top equals x stack a with ‾ on top plus y stack b with ‾ on top plus z stack c with ‾ on top$ . The range of $x plus y plus z$ is

$stack a with minus on top comma stack b with minus on top comma stack c with minus on top$ are non-coplanar vectors and $stack a with minus on top plus stack b with minus on top plus stack c with minus on top$ and $stack b with minus on top plus stack c with minus on top plus stack d with minus on top$ are collinear with $stack d with minus on top$ and $stack a with minus on top$ respectively then $stack a with minus on top plus stack b with minus on top plus stack c with minus on top plus stack d with minus on top$ is

$stack a with minus on top comma stack b with minus on top comma stack c with minus on top$ are non-coplanar vectors and $stack a with minus on top plus stack b with minus on top plus stack c with minus on top$ and $stack b with minus on top plus stack c with minus on top plus stack d with minus on top$ are collinear with $stack d with minus on top$ and $stack a with minus on top$ respectively then $stack a with minus on top plus stack b with minus on top plus stack c with minus on top plus stack d with minus on top$ is

parallel

If $a subscript 1 end subscript$ and $a subscript 2 end subscript$ are two values of a for which the unit vector $stack a i with minus on top plus b j with minus on top plus 1 half k with minus on top$ is linearly dependent with $i with minus on top plus 2 j with minus on top$ and $j with minus on top minus 2 k with minus on top$ then $fraction numerator 1 over denominator a subscript 1 end subscript end fraction plus fraction numerator 1 over denominator a subscript 2 end subscript end fraction$ is equal to

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$a with rightwards arrow on top equals left parenthesis c o s invisible function application theta right parenthesis i with rightwards arrow on top minus left parenthesis s i n invisible function application theta right parenthesis j with rightwards arrow on top comma b with rightwards arrow on top equals left parenthesis s i n invisible function application theta right parenthesis i with rightwards arrow on top plus left parenthesis c o s invisible function application theta right parenthesis j with rightwards arrow on top comma c with rightwards arrow on top equals k with rightwards arrow on top comma r with rightwards arrow on top equals 7 i with rightwards arrow on top plus j with rightwards arrow on top plus 10 k with rightwards arrow on top$ if $stack r with rightwards arrow on top equals x stack a with rightwards arrow on top plus y stack b with rightwards arrow on top plus z stack c with rightwards arrow on top$ , then

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$L t ┬ left parenthesis x rightwards arrow 0 right parenthesis left parenthesis x left parenthesis 1 plus a c o s invisible function application x right parenthesis minus b s i n invisible function application x right parenthesis divided by x cubed equals 1 t h e n a equals comma b equals$

$L t ┬ left parenthesis x rightwards arrow 0 right parenthesis left parenthesis x left parenthesis 1 plus a c o s invisible function application x right parenthesis minus b s i n invisible function application x right parenthesis divided by x cubed equals 1 t h e n a equals comma b equals$

parallel

$L t subscript left parenthesis x rightwards arrow 0 right parenthesis left parenthesis x 10 to the power of x minus x right parenthesis divided by left parenthesis 1 minus c o s invisible function application x right parenthesis equals$

For such questions, we should know different formulae.

$L t subscript left parenthesis x rightwards arrow 0 right parenthesis left parenthesis x 10 to the power of x minus x right parenthesis divided by left parenthesis 1 minus c o s invisible function application x right parenthesis equals$

For such questions, we should know different formulae.

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Chemistry-General

$L t subscript left parenthesis n rightwards arrow infinity right parenthesis left parenthesis n left parenthesis 1 cubed plus 2 cubed plus midline horizontal ellipsis. plus n cubed right parenthesis squared right parenthesis divided by left parenthesis 1 squared plus 2 squared plus midline horizontal ellipsis plus n squared right parenthesis cubed equals$

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parallel

Equivalent weight of HCHO in the following reaction $2 HCHO plus OH to the power of minus not stretchy rightwards arrow HCOO to the power of minus plus straight A$ is 30. A can be

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Chemistry-General

Which of the following statement is incorrect?

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Chemistry-General

$L t subscript left parenthesis x rightwards arrow 0 right parenthesis invisible function application 1 divided by s i n squared invisible function application x minus 1 divided by s i n h squared invisible function application x equals$

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parallel

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