Taylor Series - Example 1

[@josephsands7938]

Great explanation, this helped me with calc 3 two years later and I'm sure it will be helpful to students for years to come. Thank you for doing this.

[@ziploxian8516]

You did everything perfectly till the end where you didn't show how you did the root/ratio test and got 7 as the radius.

[@Aks_Sin]

Please,explain how the interval was obtained by ratio/root test ?

[@justsomegirlwithoutamustac5837]

he has such a gentle voice

[@slcmathpc]

:-)

[@meamarie8714]

Best explanation i've seen so far! Thanks!!!

[@hyericho441]

how is the range -5 to 9 using the root test?

[@alexramirez5104]

Thanks for the videos...they help so much!

[@davinci4032]

Great video. I have a question, how was the interval -5,9 determined?

[@slcmathpc]

You can apply either the Ratio Test or the Root Test; I have videos covering both, so you can check out my playlist on integral calculus. :-)

[@katesaychaleun6322]

I have a question: How did we figure out the interval at 12:57 ? Did I miss something? Is there some formula or approach to finding this? Additionally, why is it important to define the interval? P/S: Awesome video! Appreciated it :)

[@slcmathpc]

As mentioned in the video, one can apply the Ratio Test to determine the radius of convergence of the power series. The reason why it is important to find the interval of convergence of the series is to know when it is equal to the original function. Notice that in this case, the equality between the original function and its Taylor series does not hold for all values of x, but instead holds only if -5 < x < 9.

[@zaidelkhateeb932]

What about chain rule? Don't you have to multiply by the derivative of what's in the parenthesis?

[@tinkman98]

The derivative of (x+5) is just one because 5 is a constant and x's coefficient is just one. If it were (2x+5) you would need to multiply by an additional 2 each time.

[@SierraSlim1]

Nicely done!

[@bangmet45]

great explanation !!

[@hritabandasghosh10]

Can I get to know how You setup the camera? Good Maths though!

[@slcmathpc]

It's amazing what one can accomplish with a kid's plastic hockey stick, empty jars of peanut butter and some duct tape. ;-)

[@hritabandasghosh10]

Creativity at it's peak!

[@hritabandasghosh10]

@@slcmathpc Will you like to share your setup picture if I send my mail id?

[@williammwala7989]

Why are we using 2 as the center?

[@slcmathpc]

In this case, 2 is an arbitrary choice. In general, the center would be a point around which you are interested in the behavior of the function. For example, if you had a limit involving the function f(x) as x approaches 3 that yielded an indeterminate case, then you may investigate the limit by calculating the Taylor series expansion of f(x) centered at x=3.

[@SMABackup]

Thanks so much!

[@saptakidebnath5774]

thanks for helping me out

[@lawrenceogunjimi5002]

Good explanations

[@ognjenmladenovic9960]

Perfect!

[@monkeymoose4877]

Québécois? I feel like I notice the accent haha

[@slcmathpc]

:-)

[@asgarrahmani939]

it is must for help

[@اياتالمراد]

شرح خره