limit question

[markraz]

LIM LN(2-2x)
x->1-

How would you guys begin to solve this limit?
without a calculator or graphing utility?

do you have to plugin numbers in your head?
or is there some easier process?

thanks

 

[Bob Brown MSEE]

LIM LN(-x)= -infinity
x->0-

so answer: -infinity*2 = -infinity

 

[markraz]

LIM LN(-x)= -infinity
x->0-

so answer: -infinity*2 = -infinity

thanks but what process is used to determine this ? do I just have to memorize the graph?

 

[Deleted member 4993]

LIM LN(2-2x)
x->1-

How would you guys begin to solve this limit?
without a calculator or graphing utility?

do you have to plugin numbers in your head?
or is there some easier process?

thanks

Another way

let x = 1-ε

then

\(\displaystyle \lim_{x\to1^-}ln(2-2x) \ = \lim_{ε \to 0}ln(2ε) \ = - ∞ (or DNE)\)

Yes to some extent you have to remember the graph of ln(x) - i.e. ln(x) goes to "increasingly negative" value as x → 0⁺ (approaching from right) .............. edit

 

[Quaid]

do I just have to memorize the graph

Hi Mark,

No, we don't need to memorize the graph of y = ln(2-2x)

We need to memorize the graph of y = ln(x)

After that, it helps to understand the topic of graph transformations (from precalculus); that is, if you know the steps to go from the graph of ln(x) to the graph of ln(2-2x), then you can "see" that the general behavior of ln(2-2x) as x approaches 1 from the left is the same as the behavior of ln(x) as x approaches zero from the right.

Cheers :cool:

 

[markraz]

Hi Mark,

No, we don't need to memorize the graph of y = ln(2-2x)

We need to memorize the graph of y = ln(x)

After that, it helps to understand the topic of graph transformations (from precalculus); that is, if you know the steps to go from the graph of ln(x) to the graph of ln(2-2x), then you can "see" that the general behavior of ln(2-2x) as x approaches 1 from the left is the same as the behavior of ln(x) as x approaches zero from the right.

Cheers :cool:

thanks, so there is no way around memorizing graphs?

 

[Quaid]

ֺ

so there is no way around memorizing graphs?

There's always a way.

If you don't want to memorize the general behavior of elementary functions -- like y=e^x, y=ln(x), y=sin(x), y=arcsin(x) -- then you can reconstruct what you need to know each time, by building a table of xy-values and plotting points.

(I think that it's easier in the long run to memorize a few graphs.)

ֺ