Question

I NEED HELP PLEASE, THANKS! :)

Answer 1

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

Answer 2

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`