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    Maths-
    General
    Easy

    Question

    L t subscript x not stretchy rightwards arrow negative straight infinity end subscript open square brackets fraction numerator x to the power of 4 sin invisible function application open parentheses 1 over x close parentheses plus x squared over denominator open parentheses 1 plus vertical line x vertical line cubed close parentheses end fraction close square brackets equals

    1. 1
    2. -1
    3. 0
    4. negative straight infinity

    hintHint:

    In this question we will useA s space 1 plus vertical line x vertical line cubed equals open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell 1 plus x cubed end cell cell i f space x greater or equal than 0 end cell row cell 1 minus x cubed end cell cell i f space x less than 0 end cell end table close comma space w e space w i l l space u s e space 1 minus x cubed as the infinity is negative. Then we will divide the equation by x cubed and after simplifying we will put the value of x.

    The correct answer is: -1

      space space space space L t subscript x not stretchy rightwards arrow negative straight infinity end subscript space open square brackets fraction numerator x to the power of 4 sin invisible function application open parentheses 1 over x close parentheses plus x squared over denominator open parentheses 1 plus vertical line x vertical line cubed close parentheses end fraction close square brackets A s space 1 plus vertical line x vertical line cubed equals open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell 1 plus x cubed end cell cell i f space x greater or equal than 0 end cell row cell 1 minus x cubed end cell cell i f space x less than 0 end cell end table close equals L t subscript x not stretchy rightwards arrow negative straight infinity end subscript space space open square brackets fraction numerator x to the power of 4 sin invisible function application open parentheses 1 over x close parentheses plus x squared over denominator open parentheses 1 minus x cubed close parentheses end fraction close square brackets D i v i d i n g space b y space x cubed comma space w e space g e t colon equals L t subscript x not stretchy rightwards arrow negative straight infinity end subscript space open square brackets fraction numerator x sin space begin display style 1 over x end style plus begin display style 1 over x end style over denominator begin display style 1 over x cubed end style minus 1 end fraction close square brackets equals L t subscript x not stretchy rightwards arrow negative straight infinity end subscript space open square brackets fraction numerator begin display style fraction numerator sin space begin display style 1 over x end style over denominator begin display style 1 over x end style end fraction end style plus begin display style 1 over x end style over denominator begin display style 1 over x cubed minus 1 end style end fraction close square brackets equals fraction numerator 1 plus 0 over denominator 0 minus 1 end fraction equals negative 1.

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