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Maths-

General

Easy

Question

$Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of tan space x end exponent minus e to the power of x over denominator tan space x minus x end fraction$

0
$e^{x}$
tan x
1

hint Hint:

In this question we will simplify the equation and later put the value of x.

The correct answer is: 1

$space space space space Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of tan space x end exponent minus e to the power of x over denominator tan space x minus x end fraction equals space Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of x left parenthesis e to the power of tan space x minus x end exponent minus 1 right parenthesis over denominator tan space x minus x end fraction equals Lt subscript x not stretchy rightwards arrow 0 end subscript space e to the power of x equals e to the power of 0 equals 1.$

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