Part C of the last question of the 2018 Calculus BC exam we're almost
done let P a4 of X be the fourth degree Taylor polynomial most as excited as if
I was really taken the test for F about X is equal to 0 well I guess I
technically did but I didn't follow the you know timed interval use the
ultimatum series error bound to find the upper bound for the absolute value of P
suppor of 2 minus F of 2 now we learned two types of errors when dealing with
basically Taylor polynomials sort of like a legrasse form of the air and well
we have a nice fairly actually simple process if the series happines happens
to be alternating the alternating series remainder what the heck is this
expression about and what are they asking us to do if a convergent
alternating series satisfies the condition where a sub n plus 1 is less
than or equal to a sub n then the absolute value of the remainder R sub n
the absolute value remainder R sub n is less than or equal to the first
neglected term so the absolute value of the difference between the value of the
series minus the value that you're getting from whatever degree Taylor
polynomial that you're working with alternate well in this case alternating
series not any Taylor polynomial is equal to the absolute value of R sub n
that is the absolute value of your error and we're looking for that upper bound
of that error is well less than or equal to a sub n plus 1 the first neglected
term so what we are going to do is we're going to simply look at the fact that
this is less than or equal to what we're talking about the fourth degree Taylor
polynomial that's alternating so we just need to look at the fifth degree
basically term we're going to use this expression and how it creates that well
that fifth degree and you kind of really don't need
but I'm gonna do that for just teaching purposes anyway glancing down to my
notes to make sure I don't mess this up so this is less than or equal to the
absolute value of negative 1 to the n plus 1 well again we have the second
third and the fourth degree terms here so we're looking at the fifth degree
term so we're looking at negative 1 to the 4 plus 1 power times X and we're
looking at an x value of 2 so 2 to the n plus 1 over N which again is 4 right
yeah cuz we're for n plus 1 so 4 times 3 to the fourth power now that's going to
be negative 1 out well this absolute value so it's going to cancel that out
anyway and so we're looking at 2 to the fifth power over 4 times 3 to the fourth
or base we're looking at 32 over 3 24 and yeah so the upper bound is equal to
actually look I'm looking back and forth now I've been better just to do this if
we look at this I got 2 to the 5th is 2 4 8 16 32 4 times 3 to the 4th so 8 so
the upper bound of this error is equal to 8 3 9 27 81 and that is the end of
our 2018 Calculus BC exam or the end at least this is only video you're watching
of number 6 I'm miss a true hey go to your homework
you