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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

  1. 0
  2. e to the power of x
  3. tan x
  4. 1

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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