Question

PLEASE HELP

find the limit

limf(X), where f(x)={x^2-4x+6, x<2
z-->2 {-x^2+4x-2, x>or greater than 2

Answer 1

so u have 2 different definition of f(x) for two different range of x.
which range contains x=2 ?

Answer 2

the 1st one or the 2nd one ?

Answer 3

Evaluate each of the pieces of the piecewise function. If they're the same - that's the limit.

I assume the z should be an x.

Answer 4

both...?

Answer 5

yeah thats my bad.. z is supposed to be x

Answer 6

when you use right side limit, use upper function, and left sid limit, use below function

Answer 7

nopes, not both. the first one has x<2...not equal.
the 2nd one has x>=2....this contains x=, got it ?

Answer 8

*x=2

Answer 9

oh ok so the second one

Answer 10

so the solving idea is mine. :)

Answer 11

yup, now directly put x=2 in 2nd function, and tell me what u get?

Answer 12

2

Answer 13

no his formula is when x goes to 2 find the limit of fuction so, it must investigate left and right limitation

Answer 14

yes,thats correct.....that is your f(2)
now u need to check whether f(2) equals left hand limit and right hand limit....if so then your limit value =2
if not then limit value does not exist.
do u know how to find left hand and right hand limit ?

Answer 15

it is not to find continuous ... just find left and right limit