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Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator 11 x cubed minus 3 x plus 4 over denominator 13 x cubed minus 5 x squared minus 7 end fraction

  1. fraction numerator negative 11 over denominator 3 end fraction
  2. 11 over 13
  3. 1 over 13
  4. fraction numerator negative 1 over denominator 13 end fraction

hintHint:

In this question, we have to find  limt value of Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator 11 x cubed minus 3 x plus 4 over denominator 13 x cubed minus 5 x squared minus 7 end fraction.

The correct answer is: 11 over 13


    Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator 11 x cubed minus 3 x plus 4 over denominator 13 x cubed minus 5 x squared minus 7 end fraction
    Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator 11 x cubed minus 3 x plus 4 over denominator 13 x cubed minus 5 x squared minus 7 end fraction has indeterminate form infinity over infinity, but we can factor and reduce.
    Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator 11 x cubed minus 3 x plus 4 over denominator 13 x cubed minus 5 x squared minus 7 end fraction space W e space c a n space w r i t e space i t space l i k e space Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator 11 minus begin display style 3 over x squared end style plus begin display style 4 over x cubed end style over denominator 13 minus begin display style 5 over x end style minus begin display style 7 over x cubed end style end fraction
    On substituting, We get
    space Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator 11 minus begin display style 3 over x squared end style plus begin display style 4 over x cubed end style over denominator 13 minus begin display style 5 over x end style minus begin display style 7 over x cubed end style end fraction space equals space fraction numerator 11 minus 3 cross times 0 plus 4 cross times 0 over denominator 13 minus begin display style 5 cross times 0 minus 7 cross times 0 end style end fraction space equals 11 over 13

    Infinite limits in calculus occur when the function is unbounded and tends toward infinity or negative infinity as x approaches a given value.

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