Maths-
General
Easy

Question

L t subscript left parenthesis x rightwards arrow infinity right parenthesis invisible function application left parenthesis 3 x cubed plus 4 x plus 5 right parenthesis divided by left parenthesis 2 x cubed plus 3 x minus 7 right parenthesis

  1. 3 divided by 2  
  2. 2 divided by 3
  3. 1 divided by 2
  4. 1 divided by 3

hintHint:

We are given the function. We have to find the limit of the function.

The correct answer is: 3 divided by 2


    The given function is f open parentheses x close parentheses equals fraction numerator 3 x cubed plus 4 x plus 5 over denominator 2 x cubed plus 3 x minus 7 end fraction
    We have to find the limit of the function.
    stack li m with x rightwards arrow infinity below f open parentheses x close parentheses equals limit as x rightwards arrow infinity of fraction numerator 3 x cubed plus 4 x plus 5 over denominator 2 x cubed plus 3 x minus 7 end fraction
space space space space space space space space
I f space w e space s u b s t i t u t e space t h e space v a l u e space i f space x space w e space g e t space infinity space f o r space n u m e r a t o r
a n d space d e n o m i n a t o r. space
T o space a v o i d space t h i s comma space w e space d i v i d e space n u m e r a t o r space a n d space d e n o m i n a t o r space b y space x cubed
space limit as x rightwards arrow infinity of f left parenthesis x right parenthesis equals limit as x rightwards arrow infinity of fraction numerator 3 begin display style x cubed over x cubed end style plus 4 begin display style x over x cubed end style plus begin display style 5 over x cubed end style over denominator 2 begin display style x cubed over x cubed end style plus 3 begin display style x over x cubed end style minus begin display style 7 over x cubed end style end fraction
space space space space space space space space space space space space space space equals limit as x rightwards arrow infinity of fraction numerator 3 space plus begin display style 4 over x squared end style plus begin display style 5 over x cubed end style over denominator 2 plus begin display style 3 over x squared end style minus begin display style 7 over x cubed end style end fraction
space space space space space space space space space space space space equals limit as x rightwards arrow infinity of fraction numerator 3 space plus space begin display style 4 over open parentheses infinity close parentheses squared end style plus space begin display style 5 over open parentheses infinity close parentheses cubed end style over denominator 2 space plus space begin display style 3 over left parenthesis infinity right parenthesis squared end style minus begin display style 7 over open parentheses infinity close parentheses squared end style end fraction space space

space space space space space space
space space space space.
    Now, we know that
    table attributes columnalign left end attributes row cell 1 over open parentheses infinity close parentheses squared equals 0 end cell row cell 1 over open parentheses infinity close parentheses cubed equals 0 end cell end table
    So,
    limit as x rightwards arrow 0 of f open parentheses x close parentheses equals limit as x rightwards arrow 0 of fraction numerator 3 space plus space 0 space plus space 0 over denominator 2 space plus space 0 space plus space 0 end fraction
space space space space space space space space space space space space space space equals 3 over 2
    This is the final answer.

    For such questions, we should know different formulas of limit.

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