Question

How to find the limits from graph?

Answer 1

just find value of points around the point at which you want to find the limit. take the arbitrary point as close as you can to the point at which you wanna find limit. that would be your value of limit since limit doesn't care what is going at the exact point. limit just tells you what is happening around the point

Answer 2

I want to know the answer of the following

Answer 3

Well ill do one or two and then you'll get it by then :)

\(\lim_{x\rightarrow0^-}\) Is very similar to saying that what does the function approach as the x value moves very close from the indicated direction. So if you move your finger along the graph slowly from any negative x value towards zero (since we are approaching from the negative) you will see it approaches the line \(y=5\). So therefore,
\[\lim_{x\rightarrow0^-}=+5\]

Answer 4

Similarly if you approach it from the positive x side, you will approach the line of \(y=-5\) so therefore, we say:
\[\lim_{x\rightarrow0^+}f(x)=-5\]

Answer 5

WOW !! You are genius ! my teacher tried to make me understand thousand times but failed!

Answer 6

Thanks budy

Answer 7

Hehehe thanks man anytime!

Answer 8

Is this for highschool calc or first year...? or what course is this for?

Answer 9

yes high school calculus !

Answer 10

Ahh I see cool man! If you want, you can "fan me" and whenever you need another question, just tag me like this:
"@keithafascalclover"

Answer 11

One more question

Answer 12

@KeithAfasCalcLover

Answer 13

@keithafascalclover please answer another question.

Answer 14

Hey g.dev haha sorry about that I got caught up on something else haha

The limits are a little fuzzy at the bottom...can you re-upload?

Answer 15

\[\lim_{x \rightarrow -1}\], \[\lim_{x \rightarrow +1} \], \[\lim_{x \rightarrow 1}\]
\[\lim_{x \rightarrow -0}\] \[\lim_{x \rightarrow +0}\] , \[\lim_{x \rightarrow 0}\]

Answer 16

@keithafascalclover

Answer 17

Beauty! haha okay lets get started!

Answer 18

For the first one I assume you mean:
\[\lim_{x\rightarrow1^-}f(x)\]
not
\[\lim_{x\rightarrow-1}f(x)\]
So then we notice that the graph is approaching in interesting limit haha. If you try following the graph towards 1 from the negative side, you'll have a little difficulty. We notice that it approaches a big number...REALLY big. In calculus, we use \(\infty\) to represent a really big number. so then we say that:
\[\lim_{x\rightarrow1^-}f(x)=+\infty\]

Answer 19

and similarly when the limit is tending x towards negative zero, the graph is reaching at y = -2 so the limit is -2 right?

Answer 20

RIGHT!
\[\lim_{x\rightarrow-0}=-2\]

Answer 21

thanks brother may god bless you!

Answer 22

God Bless you too!
Just to point out, if:
\[\lim_{x\rightarrow a^-}f(x)=\lim_{x\rightarrow a^+}f(x)=L\]
Then we can say that:
\[L=\lim_{x\rightarrow a}\]

Answer 23

In other words if the limit from the negative is the same as the limit from the positive, then we can drop the positive and negative signs

Answer 24

Good Luck with your studies and god bless!