Maths-
General
Easy

Question

L t subscript left parenthesis x rightwards arrow 3 right parenthesis invisible function application left parenthesis 4 x squared minus 17 x plus 15 right parenthesis divided by left parenthesis x squared minus x minus 6 right parenthesis

  1. 1 divided by 5
  2. left parenthesis negative 1 right parenthesis divided by 5
  3. space 7 divided by 5
  4. left parenthesis negative 7 right parenthesis divided by 5

hintHint:

We are given a function. We have to find the limit of the function. We have to adjust the function in a way that on substituting the limit, we don't get zero.

The correct answer is: space 7 divided by 5


    The given function is f left parenthesis x right parenthesis space equals fraction numerator 4 x squared minus 17 x plus 15 over denominator x squared minus x minus 6 end fraction
    We have to find the limit of the function.
    limit as x rightwards arrow 3 of f open parentheses x close parentheses equals limit as x rightwards arrow 3 of fraction numerator 4 x squared minus 17 x space plus space 15 over denominator x squared minus x space minus 6 end fraction
I f space w e space s u b s t i t u t e space x space equals space 3 comma space w e space g e t space z e r o space v a l u e space o f space t h e space l i m i t.

S o comma space w e space w i l l space f a c t o r i s 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 space 4 x squared minus 17 x space plus space 15 space equals space 4 x squared minus 12 x space minus 5 x space plus 15
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 4 x left parenthesis x space minus space 3 right parenthesis minus 5 left parenthesis x space minus space 3 right parenthesis
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space left parenthesis 4 x minus 5 right parenthesis left parenthesis x minus 3 right parenthesis
space space space space space x squared minus x minus 6 space equals space x squared minus 3 x plus 2 x minus 6
space space space space space space space space space space space space space space space space space space space space space space equals x left parenthesis x minus 3 right parenthesis plus 2 left parenthesis x minus 3 right parenthesis
space space space space space space space space space space space space space space space space space space space space space space equals left parenthesis x space plus space 2 right parenthesis left parenthesis x space minus space 3 right parenthesis

limit as x rightwards arrow 3 of f left parenthesis x right parenthesis space equals limit as x rightwards arrow 3 of fraction numerator left parenthesis 4 x space minus 5 right parenthesis left parenthesis x space minus 3 right parenthesis over denominator left parenthesis x plus 2 right parenthesis left parenthesis x minus 3 right parenthesis end fraction
space space space space space space space space space space space space space space equals limit as x rightwards arrow 3 of fraction numerator 4 x space minus 5 over denominator x space plus space 2 end fraction
space space space space space space space space space space space space space space equals space fraction numerator 4 left parenthesis 3 right parenthesis space minus space 5 over denominator 3 plus space 2 end fraction
space space space space space space space space space space space space space space equals 7 over 5
space space space space
    This is the final answer.

    For such questions, we should know different formulas of limits. We should try different methods to simplify the function in a way that it doesn't become zero.

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