Maths-
General
Easy

Question

Lt subscript x not stretchy rightwards arrow 0 end subscript space x squared cos space 2 over x

  1. 1
  2. 0
  3. does not exist

  4. none of these

hintHint:

Trigonometry is one of the branches of mathematics. There are six trigonometric functions and the limit of each of these functions leading to the point. However, we can calculate the limits of these functions according to the continuity of the function, considering the domain and range of trigonometric functions.
In this question, we have to find value of Lt subscript x not stretchy rightwards arrow 0 end subscript space x squared cos space 2 over x.

The correct answer is: 0


    Lt subscript x not stretchy rightwards arrow 0 end subscript space x squared cos space 2 over x

    Lt subscript x not stretchy rightwards arrow 0 end subscript space x squared cos space 2 over x space cross times fraction numerator 2 space cross times space sin space begin display style 2 over x end style over denominator 2 space cross times space sin space begin display style 2 over x end style end fraction space equals L t subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator 2 space cross times space sin space begin display style 2 over x space cos space 2 over x space cross times space x squared end style over denominator 2 space cross times space sin space begin display style 2 over x end style end fraction
L t subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator x squared sin space begin display style 4 over x space end style over denominator 2 space cross times space sin space begin display style 2 over x end style end fraction space cross times 2 over 2
L t subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator 2 x sin space begin display style 4 over x space end style over denominator begin display style 4 over x end style space cross times space sin space begin display style 2 over x end style end fraction space equals space L t subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator sin space begin display style 4 over x space end style over denominator begin display style 4 over x space end style end fraction cross times space L t subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator 2 x over denominator begin display style sin space 2 over x end style end fraction
    space L t subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator left parenthesis begin display style 2 over x end style right parenthesis x squared over denominator begin display style sin space 2 over x end style end fraction =space L t subscript x not stretchy rightwards arrow 0 end subscript space x squared = 0

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