How do you find One Sided Limits Algebraically?

In this discussion, we are going to algebraically evaluate left and right-hand limits, also known as one-sided limits.

The following are the examples I discuss:

🔹limx→−2+(x+3)|x+2|x+2

🔹limx→−2−(x+3)|x+2|x+2

🔹limx→−2(x+3)|x+2|x+2

Keep in mind the following:

limx→c+f(x)=limh→0+f(c+h)

limx→c−f(x)=limh→0+f(c−h)

Note that, in both cases, h approaches 0 from the right because h is always positive.

However, as x approaches c from the right,

we plug in x + positive h.

As x approaches c from the left,

we plug in x – positive h

Another thing to keep in mind is that 

if 

limx→c+f(x)=limx→c−f(x)=L

then 

limx→cf(x)=L

Also if

limx→c+f(x)≠limx→c−f(x)

then

limx→cf(x)D.N.E

🔹Example 1:

limx→−2+(x+3)|x+2|x+2

🔹Example 2:

limx→−2−(x+3)|x+2|x+2

limx→−2−(x+3)|x+2|x+2

🔹Example 3

limx→−2(x+3)|x+2|x+2

The limit does not exist because, as seen in example 1 and 2, the left-hand limit does not equal the right-hand limit.

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There is more where that came from.

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Angela Morgan