Maths-
General
Easy

Question

L t subscript left parenthesis x rightwards arrow infinity right parenthesis invisible function application left parenthesis left parenthesis x plus 6 right parenthesis divided by left parenthesis x plus 1 right parenthesis right parenthesis to the power of left parenthesis x plus 4 right parenthesis equals

  1. e to the power of 6
  2. e to the power of 4
  3. e
  4. e cubed

hintHint:

In this question we are getting 1 to the power of infinity form.. So, we will use the standard limit limit as x rightwards arrow infinity of left parenthesis f left parenthesis x right parenthesis to the power of g left parenthesis x right parenthesis end exponent equals space e to the power of limit as x rightwards arrow infinity of left parenthesis f left parenthesis x right parenthesis minus 1 right parenthesis g left parenthesis x right parenthesis end exponent to find the limit.

The correct answer is: e cubed


    In this question we have to find the limit of limit as x rightwards arrow infinity of open parentheses fraction numerator x plus 6 over denominator x plus 1 end fraction close parentheses to the power of left parenthesis x plus 4 right parenthesis end exponent
    Step1: Putting the value of limit in the expression.
    By putting the value of limit we are get 1 to the power of infinity form.
    Step2: Using Standard limits
    We know that limit as x rightwards arrow infinity of left parenthesis f left parenthesis x right parenthesis to the power of g left parenthesis x right parenthesis end exponent equals space e to the power of limit as x rightwards arrow infinity of left parenthesis f left parenthesis x right parenthesis minus 1 right parenthesis g left parenthesis x right parenthesis end exponent
    =>e to the power of limit as x rightwards arrow infinity of open parentheses fraction numerator x plus 6 over denominator x plus 1 end fraction minus 1 close parentheses left parenthesis x plus 4 right parenthesis end exponent
    => e to the power of limit as x rightwards arrow infinity of open parentheses fraction numerator x plus 6 minus x minus 1 over denominator x plus 1 end fraction close parentheses left parenthesis x plus 4 right parenthesis end exponent
    => e to the power of limit as x rightwards arrow infinity of 5 cross times open parentheses fraction numerator x plus 4 over denominator x plus 1 end fraction close parentheses end exponent
    => e to the power of limit as x rightwards arrow infinity of 5 cross times open parentheses fraction numerator 1 plus begin display style 4 over x end style over denominator 1 plus begin display style 1 over x end style end fraction close parentheses end exponent
    Step3: Putting the value of limit
    =>e to the power of 5
    Hence, the value of limit is e to the power of 5.

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.