SOLUTION: please help f(x)=(x�-4)/|x-2| find each limit (if possible) a) lim as x→2 from left f(x) b)lim as x→2 from right f(x) c)lim as x→2 f(x)

Question 1090027: please help
f(x)=(x�-4)/|x-2| find each limit (if possible)
a) lim as x→2 from left f(x)
b)lim as x→2 from right f(x)
c)lim as x→2 f(x)
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The function is
or
The function is clearly undefined at x=2, since the denominator will be 0. The limit as x approaches 2 will exist if and only if the limits as you approach 2 both from the left and from the right are the same.
For values of x less than 2, |x-2| = -(x-2), so

so the function is equivalent to -(x+2), or
f(x) = -x-2
So as you approach 2 from the left, the function value approaches
-2-2 = -4
For values of x greater than 2, |x-2| = (x-2), so

so the function is equivalent to
f(x) = 1(x+2) = x+2
So as you approach 2 from the left, the function value approaches
2+2 = 4
So the answers are
a) the limit as x approaches 2 from the left is -4
b) the limit as x approaches 2 from the right is 4
c) the limit as x approaches 2 does not exist, because the limits from
the left and right are not the same

RELATED QUESTIONS
Consider f(x) = {x^2−1, x < 1 f(x) = {0, 1 < x ≤ 3 f(x) =... (answered by solver91311)

For each of the limits determine whether the limit exists as a number, as an infinite... (answered by Boreal)

what's the limit: lim f(x){{{ (square root of x-2)/((x^2)-4)}}} as x approaches 2 from... (answered by solver91311)

I am very confused with the end behavior of a Polynomial. Someone please help me with... (answered by richard1234)

Evaluate the limit. (If an answer does not exist, enter DNE.) lim (9x/tan(x))... (answered by MathLover1)

Given that −x^2−2x−4 ≤ f(x) ≤ x^2+2x−2 for all x,... (answered by solver91311)

Do you think you could help me find these limits? Really appreciate your help, in... (answered by Edwin McCravy)

lim f(x) x... (answered by Fombitz)

Find a function that satisfies the given conditions. (The answers here are not unique.... (answered by solver91311)

SOLUTION: please help f(x)=(x�-4)/|x-2| find each limit (if possible) a) lim as x&#8594;2 from left f(x) b)lim as x&#8594;2 from right f(x) c)lim as x&#8594;2 f(x)

SOLUTION: please help f(x)=(x�-4)/|x-2| find each limit (if possible) a) lim as x→2 from left f(x) b)lim as x→2 from right f(x) c)lim as x→2 f(x)