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Question

L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator tan cubed begin display style space end style x minus sin cubed space x over denominator x cubed end fraction

  1. 3 over 2
  2. 1 half
  3. 5 over 2
  4. 0

hintHint:

In this question, we have to find value of  L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator tan cubed begin display style space end style x minus sin cubed space x over denominator x cubed end fraction.

The correct answer is: 3 over 2


    L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator tan cubed begin display style space end style x minus sin cubed space x over denominator x cubed end fraction
    L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator tan cubed begin display style space end style x minus sin cubed space x over denominator x cubed end fraction space equals space L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator tan cubed begin display style space end style x over denominator x cubed end fraction minus L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator sin cubed space x over denominator x cubed end fraction
left parenthesis space 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 tan cubed x over denominator x cubed end fraction equals space 1 space comma L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator sin cubed space x over denominator x cubed end fraction equals 1 space right parenthesis
1 minus 1 equals space 0

    Direct substitution can sometimes be used to calculate the limits for functions involving trigonometric functions.

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