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Some Calculus questions

Anonymous Wed 12 Aug 04:29:09 2020 No.11999637 View Reply Original Report

Quoted By: >>11999645 >>11999690 >>12000120

How do you make a derivative of a graph? Like if someone provides you a graph and then asks you to make a derivative version of it how to you find that? Also how do you know if a point on a graph is discontinuous or not? How would you state if a point is continuous or discontinuous?

Anonymous

Anonymous Wed 12 Aug 2020 04:35:07 No.11999645 Report

Quoted By: >>11999718 >>12000249 >>12000656

>>11999637
>How do you make a derivative of a graph?
Plot the derivate
>Also how do you know if a point on a graph is discontinuous or not?
The limit exists
>How would you state if a point is continuous or discontinuous?
Check if the limit exists

Anonymous

Anonymous Wed 12 Aug 2020 04:50:15 No.11999668 Report

Quoted By:

What u want is apostols calculus

!HvKi......

!HvKi...... Wed 12 Aug 2020 05:02:26 No.11999690 Report

Quoted By:

>>11999637
>How do you make a derivative of a graph? Like if someone provides you a graph and then asks you to make a derivative version of it how to you find that?
Go along the line. If the graph is increasing draw the derivative line positive. If the graph is increasing a lot draw the derivative more positive. If its decreasing draw it negative. If there is a turning point go through the x axis

Anonymous

Anonymous Wed 12 Aug 2020 05:18:48 No.11999718 Report

Quoted By: >>12000045

>>11999645
Limits are half of the answer, you can have points that are discontinuous and which both side limits exist and coincide.

Anonymous

Anonymous Wed 12 Aug 2020 07:54:50 No.12000045 Report

Quoted By: >>12000796

>>11999718
Not true, you're going to have to give an example if you really think you're right here.

Anonymous

Anonymous Wed 12 Aug 2020 08:27:12 No.12000120 Report

Quoted By:

>>11999637
>How do you make a derivative of a graph?
by hand? start with finding your critical points (derivative = 0). decide if the derivative is either positive or negative on either side. then try to fill in the blanks with something reasonable. you can increase accuracy by eyeballing the slope at a few different places.

>Also how do you know if a point on a graph is discontinuous or not?
definition of continuous at a point is that the limit exists and the function equals the limit at the point in question. if the function is discontinous, you'll have either a
>jump discontinuity == obvious
>infinite discontinuity == obvious
>removable discontinuity == obvious when marked (usually a little unfilled o)
>"essential" discontinuity == like 1/sin(x)

Anonymous

Anonymous Wed 12 Aug 2020 09:40:11 No.12000249 Report

Quoted By: >>12000730

>>11999645
>The limit exists
what do you mean with that? Once you find the limit then what?

Anonymous

Anonymous Wed 12 Aug 2020 12:07:50 No.12000656 Report

Quoted By: >>12000730

>>>11999645
>>The limit exists
what do you mean with that? Once you find the limit then what?

Anonymous

Anonymous Wed 12 Aug 2020 12:46:38 No.12000730 Report

Quoted By:

>>12000656
>>12000249
>The limit exists
>what do you mean with that?
that it's not undefined (e.g. not infinity), that (for 1d real functions) both the left and right limits exist, and that those limits equal each other

>Once you find the limit then what?
check to see if the limit equals the function at the point in question. if it does, the function is continuous. if it doesn't, you have a removable or jump discontinuity.

Anonymous

Anonymous Wed 12 Aug 2020 13:14:54 No.12000796 Report

Quoted By: >>12001824

>>12000045

I'm not the anon you're replying to, but: https://mathworld.wolfram.com/RemovableDiscontinuity.html

Anonymous

Anonymous Wed 12 Aug 2020 19:58:22 No.12001824 Report

Quoted By:

>>12000796
This, a function is continuous only if lim f(x) x-> a- = lim f(x) x -> a+ = f(a)

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