Maths-
General
Easy

Question

L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator sin begin display style space end style open parentheses pi cos squared space x close parentheses over denominator x squared end fraction is equal to

  1. straight pi
  2. negative straight pi
  3. straight pi over 2
  4. 1

hintHint:

In this question, we have to find value of L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator sin begin display style space end style open parentheses pi cos squared space x close parentheses over denominator x squared end fraction.

The correct answer is: straight pi


    L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator sin begin display style space end style open parentheses pi cos squared space x close parentheses over denominator x squared end fraction
    L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator sin begin display style space end style open parentheses pi cos squared space x close parentheses over denominator x squared end fraction space space space space space space space left parenthesis space W e space c a n space w r i t e space cos squared x space equals space 1 space minus space sin squared x space right parenthesis
    L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator sin begin display style space end style open parentheses pi left parenthesis 1 minus s i n squared space x right parenthesis close parentheses over denominator x squared end fraction cross times fraction numerator pi sin squared space x over denominator pi sin squared space x end fraction space equals space L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator sin begin display style space end style open parentheses pi minus straight pi sin squared space x close parentheses over denominator pi sin squared space x end fraction cross times fraction numerator pi s i n squared space x over denominator x squared end fraction
left parenthesis W e space k n o w space t h a t space L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator sin begin display style space end style open parentheses x close parentheses over denominator space x end fraction space equals space 1 space right parenthesis
space L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator pi sin squared space x over denominator x squared end fraction space equals space L subscript x not stretchy rightwards arrow 0 end subscript space straight pi space equals straight pi

    The substitution rule for calculating limits is a method of finding limits, by simply substituting the value of x with the point at which we want to calculate the limit.

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