Respuesta :

bekkarmahdi702

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
  • [tex]\lim_{x\to \5} \frac{x^{2} -3x-10}{2x-10}[/tex] = 7/2

leena

Hey there! :)

Answer:

[tex]\lim_{x \to 5} = 7/2[/tex]

Step-by-step explanation:

We are given the equation:

[tex]\frac{x^{2}-3x-10 }{2x-10}[/tex]

Factor the numerator and denominator:

[tex]\frac{(x - 5)(x+2) }{2(x-5)}[/tex]

'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:

[tex]\frac{((5)+2) }{2}[/tex] = 7/2

Therefore:

[tex]\lim_{x \to 5} = 7/2[/tex]

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