Consider the Taylor polynomial T n ( x ) centered at x = 21 for all n for the function f ( x ) = 1 x − 1 , where i is the index of summation. Find the i th term of T n ( x ) . (Express numbers in exact form. Use symbolic notation and fractions where needed. For alternating series, include a factor of the form ( − 1 ) n in your answer.)

Step-by-step explanation:

Remember the geometric series

So we can express

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb

the correct answer is b.

this is because an open circle means < or > & since the line goes left it is < -3.

the next one has a filled circle so it can only be ≥ or ≤ and since the line goes right from 1 it is ≥ 1

hope that