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General

Easy

Question

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x plus a over denominator x plus b end fraction close parentheses to the power of x plus b end exponent equals$

$e^{e - b}$
$e^{a + b}$
$e^{a t}$
$e^{\frac{6}{b}}$

hint Hint:

To solve the given function, we will use the formula $limit as x rightwards arrow infinity of left parenthesis f left parenthesis x right parenthesis right parenthesis to the power of g left parenthesis x right parenthesis end exponent equals e to the power of stack lim with x rightwards arrow infinity below g left parenthesis x right parenthesis left parenthesis f left parenthesis x right parenthesis minus 1 right parenthesis end exponent$ after using the formula we will solve the function till that stage when putting the value of x will not make the function undefined, later we will put the value of x and get the required answer.

The correct answer is: $e to the power of e minus b end exponent$

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x plus a over denominator x plus b end fraction close parentheses to the power of x plus b end exponent w h e r e comma space f left parenthesis x right parenthesis equals open parentheses fraction numerator x plus a over denominator x plus b end fraction close parentheses space a n d space g left parenthesis x right parenthesis space equals left parenthesis x plus b right parenthesis w e space k n o w space t h a t space limit as x rightwards arrow infinity of left parenthesis f left parenthesis x right parenthesis right parenthesis to the power of g left parenthesis x right parenthesis end exponent equals e to the power of stack lim with x rightwards arrow infinity below g left parenthesis x right parenthesis left parenthesis f left parenthesis x right parenthesis minus 1 right parenthesis end exponent rightwards double arrow e to the power of limit as x rightwards arrow infinity of end exponent left parenthesis x plus b right parenthesis open parentheses fraction numerator x plus a over denominator x plus b end fraction minus 1 close parentheses rightwards double arrow e to the power of limit as x rightwards arrow infinity of end exponent open parentheses x plus b close parentheses open parentheses fraction numerator x plus a minus x minus b over denominator x plus b end fraction close parentheses rightwards double arrow e to the power of limit as x rightwards arrow infinity of end exponent left parenthesis a minus b right parenthesis rightwards double arrow e to the power of open parentheses a minus b close parentheses end exponent$

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