Maths-
General
Easy

Question

Lt subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses fraction numerator x squared plus 5 x plus 3 over denominator x squared plus x plus 2 end fraction close parentheses to the power of x equals

  1. e to the power of 4
  2. e cubed
  3. e squared
  4. e to the power of t

Hint:

To solve the given function, we will use the formula limit as x rightwards arrow infinity of left parenthesis f left parenthesis x right parenthesis right parenthesis to the power of g left parenthesis x right parenthesis end exponent equals e to the power of stack lim with x rightwards arrow infinity below g left parenthesis x right parenthesis left parenthesis f left parenthesis x right parenthesis minus 1 right parenthesis end exponent after using the formula we will solve the function till that stage when putting the value of x will not make the function undefined, later we will put the value of x and get the required answer.

The correct answer is: e to the power of 4


    Lt subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses fraction numerator x squared plus 5 x plus 3 over denominator x squared plus x plus 2 end fraction close parentheses to the power of x
w h e r e space f left parenthesis x right parenthesis equals open parentheses fraction numerator x squared plus 5 x plus 3 over denominator x squared plus x plus 2 end fraction close parentheses space a n d space g left parenthesis x right parenthesis equals space x
n o w space w e space k n o w space t h a t space limit as x rightwards arrow infinity of open parentheses f left parenthesis x right parenthesis close parentheses to the power of g left parenthesis x right parenthesis end exponent equals e to the power of limit as x rightwards arrow infinity of g left parenthesis x right parenthesis left parenthesis f left parenthesis x right parenthesis minus 1 right parenthesis end exponent
equals e to the power of limit as x rightwards arrow infinity of x. open parentheses fraction numerator x squared plus 5 x plus 3 over denominator x squared plus x plus 2 end fraction minus 1 close parentheses end exponent
equals e to the power of limit as x rightwards arrow infinity of x. open parentheses fraction numerator x squared plus 5 x plus 3 minus x squared minus x minus 2 over denominator x squared plus x plus 2 end fraction close parentheses end exponent
equals e to the power of limit as x rightwards arrow infinity of x. open parentheses fraction numerator 4 x plus 1 over denominator x squared plus x plus 2 end fraction close parentheses end exponent
equals e to the power of limit as x rightwards arrow infinity of. open parentheses fraction numerator 4 x squared plus x over denominator x squared plus x plus 2 end fraction close parentheses end exponent
equals e to the power of limit as x rightwards arrow infinity of x. open parentheses fraction numerator 4 plus begin display style 1 over x end style over denominator 1 plus begin display style 1 over x end style plus begin display style 2 over x squared end style end fraction close parentheses space space space space space space end exponent open square brackets d i v i n g 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 squared close square brackets
equals e to the power of 4

    Book A Free Demo

    +91

    Grade*