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I NEED HELP PLEASE, THANKS! :)

I NEED HELP PLEASE, THANKS! :)-example-1

2 Answers

7 votes

Answer:

7/2

Step-by-step explanation:

notice that if you substitute x by five you get 0/0 wich a non-defined form

The trick is to simplify by x-5

  • (x²-3x-10)/(2x-10)
  • You get using the Euclidien division : x²-3x-10 = (x-5) (x-2)
  • so : (x-2)(x-5)/2*(x-5) = (x-2)/2
  • substitute x by 5 to get 7/2

  • \lim_(x\to \5) (x^(2) -3x-10)/(2x-10) = 7/2

User Vighanesh Gursale
by
7.9k points
4 votes

Hey there! :)

Answer:


\lim_(x \to 5) = 7/2

Explanation:

We are given the equation:


(x^(2)-3x-10 )/(2x-10)

Factor the numerator and denominator:


((x - 5)(x+2) )/(2(x-5))

'x - 5' is on both the numerator and denominator, so it gets cancelled out and becomes a "hole".

This means that at x = 5, there is a hole. There is a limit at x ⇒ 5. Find the hole by plugging 5 into the simplified equation:


(((5)+2) )/(2) = 7/2

Therefore:


\lim_(x \to 5) = 7/2

User Ed Harper
by
8.4k points

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