MATH GIRL by Dr. Veselin Jungic http://www.math.sfu.ca/~vjungic/
Hi I'm MathGirl, a protector of calculopolis.
I help calculopolates who need to find the instantanious rate of change
or who need to perform approximations of some of those nasty functions.
but some people don't understand me and mistake me for a villain.
These are the two fathers of calculus Newton and Leibniz, but that's a long story.
I'd rather tell you how I use calculus to save my friend Pat.
This is my linear approximator or you can think of it as a segment of a straight line.
It's very fun to use because you only need multiplication addition and a little bit of calculus,
to get you to weird places, you don't always get to exactly where you wish but sometime close enough is good enough.
Once upon a time, I was here in my problem solving room when
That sounds like Pat Thagoras, he's stuck on square root axe mountain !
Those non-square numbers can make some places on square root axe mountain very difficult to get you.
I'll use my linear approximator.
I summon the power of Descartes
creator of XY-coordinates !
Hurry I'm falling !
Look Pat's x-coordinate is 37.
Since the first derivative of y=sqrt(x) is y'=1/(2sqrt(x)),
my linear approximator
easily jumps from perfect square to perfect square.
36 is the closest to Pat's coordinates. Is it close enough to save him ?
Let's see !
Hurry I'm falling !
Almost there Pat, let's take a closer look !
Now if my linear approximator is at the point (36,sqrt(36))=(36,6)
it will coincide with the tangent line of the function y=sqrt(x) at that point.
The distance between us will be very small, close to the differantial
My arm is long enough.
I'll save you Pat ! Grab my hand !
Thanks MATHGIRL ! My math teacher was right math is useful !
I think I should wake up and pay more attention in math class.
See close enough was good enough !
Ahh Y.. you wanna go get something to eat ?
Synchro & Transcript by KBIDA Abdellatif special thanks Hausermann Christophe and Schultz Hannah.