Maths-
General
Easy

Question

Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator x times 2 to the power of x minus x over denominator 1 minus cos space x end fraction

  1. log space 2
  2. 1
  3. log space 4
  4. 0

Hint:

In this question, we will simplify and get the required value.

The correct answer is: 2 log space 2


    space space space Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator x times 2 to the power of x minus x over denominator 1 minus cos space x end fraction
equals Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator x times left parenthesis 2 to the power of x minus 1 right parenthesis over denominator 1 minus cos space x end fraction
equals Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator x squared over denominator 1 minus cos space x end fraction. fraction numerator 2 to the power of x minus 1 over denominator x end fraction
equals Lt subscript x not stretchy rightwards arrow 0 end subscript space 4 cross times fraction numerator begin display style x squared over 4 end style over denominator 2 sin squared begin display style x over 2 end style end fraction. fraction numerator 2 to the power of x minus 1 over denominator x end fraction
equals 2 space log space 2.

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