Question

Find the limit

1 does not exist
2 )5
3)2
4)-1
5)1

Answer 1

limit = 5

Explanation:

given

lim ( x → 3)
`(x^2-x-6)/(x-3)`

if x = 3 is substituted into the expression

`(3^2-3-6)/(3-3)` =
`(9-3-6)/(3-3)` =
`(0)/(0)` ← undefined

factorising the numerator , gives

`((x-3)(x+2))/(x-3)` ( cancel x- 3 on numerator and denominator )

= x + 2

Then

lim (x → 3 ) x + 2 = 3 + 2 = 5