Maths-
General
Easy

Question

L t subscript left parenthesis x rightwards arrow infinity right parenthesis invisible function application left parenthesis 8 vertical line x vertical line plus 3 x right parenthesis divided by left parenthesis 3 vertical line x vertical line minus 2 x right parenthesis

  1. 11
  2. 10
  3. 8
  4. 5

hintHint:

We are given a function. We have to find it's limit.

The correct answer is: 11


    The given function is
    f open parentheses x close parentheses equals fraction numerator 8 vertical line x vertical line plus 3 x over denominator 3 vertical line x vertical line minus 2 x end fraction
    limit as x rightwards arrow infinity of f open parentheses x close parentheses equals limit as x rightwards arrow infinity of fraction numerator 8 vertical line x vertical line plus 3 x over denominator 3 vertical line x vertical line minus 2 x end fraction
space space space space space space space space space
    We have to find the limit of the function when x tends to infinity.
    Before that,
    |x| will have postive values for x>0 and negative values of x<0.
    |x| = x       x > 0
    |x| = -x      x < 0
    The limit is x tends to positive infinity. So, the values will be positive.
    So, for this question |x| = x
    limit as x rightwards arrow infinity of f open parentheses x close parentheses equals limit as x rightwards arrow infinity of fraction numerator 8 x plus 3 x over denominator 3 x minus 2 x end fraction

I f space w e space s u b s t i t u t e space v a l u e space o f space x space w e space g e t space infinity over infinity
S o comma space w e space w i l l space u s e space L apostrophe H o s p i t a l s space r u l e
    limit as x rightwards arrow a of fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction equals limit as x rightwards arrow a of fraction numerator f to the power of apostrophe open parentheses x close parentheses over denominator g to the power of apostrophe open parentheses x close parentheses end fraction
    limit as x rightwards arrow infinity of f open parentheses x close parentheses equals limit as x rightwards arrow infinity of fraction numerator 8 open parentheses 1 close parentheses plus 3 open parentheses 1 close parentheses over denominator 3 open parentheses 1 close parentheses minus 2 open parentheses 1 close parentheses end fraction
space space space space space space space space space space space space space space space equals limit as x rightwards arrow infinity of 11 over 1
space space space space space space space space space space space space space space space equals 11
    This is the final answer.

    For such questions, we should know different rules and formulae of limits.

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