Maths-
General
Easy

Question

L t subscript left parenthesis x rightwards arrow 3 right parenthesis invisible function application left parenthesis x cubed minus 8 x squared plus 45 right parenthesis divided by left parenthesis 2 x squared minus 3 x minus 9 right parenthesis

  1. space 7 divided by 3
  2. left parenthesis negative 7 right parenthesis divided by 3
  3. 1 divided by 3
  4. left parenthesis negative 1 right parenthesis divided by 3

hintHint:

In this question we are getting 0 over 0 form. So, we will differentiate both numerator and denominator to find the limit.

The correct answer is: left parenthesis negative 7 right parenthesis divided by 3


    In this given question we have to find limit of limit as x minus greater than 3 of fraction numerator x cubed minus 8 x squared plus 45 over denominator 2 x squared minus 3 x minus 9 end fraction
    Step1: Finding the limit.
    The limit can be found out by differentiating both numerator and denominator as we are getting 0 over 0 form.
    => limit as x minus greater than 3 of fraction numerator 3 x squared minus 16 x over denominator 4 x minus 3 end fraction
    Now we will put the value of x equals 3 in both numerator and denominator to find the limit.
    => limit as x minus greater than 3 of fraction numerator 3 cross times 3 squared minus 16 cross times 3 over denominator 4 cross times 3 minus 3 end fraction
    => fraction numerator negative 21 over denominator 9 end fraction
    =>fraction numerator negative 7 over denominator 3 end fraction.
    So, the value of the limit is fraction numerator negative 7 over denominator 3 end fraction

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