Step-by-step explanation:
The Taylor series expansion is:
Tₙ(x) = ∑ f⁽ⁿ⁾(a) (x − a)ⁿ / n!
f(x) = 1/x, a = 4, and n = 3.
First, find the derivatives.
f⁽⁰⁾(4) = 1/4
f⁽¹⁾(4) = -1/(4)² = -1/16
f⁽²⁾(4) = 2/(4)³ = 1/32
f⁽³⁾(4) = -6/(4)⁴ = -3/128
Therefore:
T₃(x) = 1/4 (x − 4)⁰ / 0! − 1/16 (x − 4)¹ / 1! + 1/32 (x − 4)² / 2! − 3/128 (x − 4)³ / 3!
T₃(x) = 1/4 − 1/16 (x − 4) + 1/64 (x − 4)² − 1/256 (x − 4)³
f(x) = 1/x has a vertical asymptote at x=0 and a horizontal asymptote at y=0. So we can eliminate the top left option. That leaves the other three options, where f(x) is the blue line.
Now we have to determine which green line is T₃(x). The simplest way is to notice that f(x) and T₃(x) intersect at x=4 (which makes sense, since T₃(x) is the Taylor series centered at x=4).
The bottom right graph is the only correct option.
Answer:
1/12
Step-by-step explanation:
Given that
30/360 to lowest fraction equivalent
Now, we can write 30 as 3×10
Also, we can write 360 as 36×10
Then, we have
(3×10)/(36×10)
Then, 10 cancel 10, we are left with
3/36
Also we can write 36 as 12×3
Then, we have
3/(12×3)
Also, 3 cancel 3, we are left with
1/12
Then the lowest fraction is 1 / 12
1/12
Answer:
I might be 560
Step-by-step explanation:
35x16
4/7 is the simplest form
You can divide 20 by 5 and get 4 and divide 35 by 5 and get 7
Answer:
66n-31m
Step-by-step explanation:
26n-7m+4(10n-6m)
26n-7m+40n-24m
66n-31m
