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.
Step-by-step explanation:
the question is not correct
edit it and I will answer u in comments
I’m pretty sure $1,800 Because if you subtract 660 by 470 you get 190 and it you multiply 190 by 6 years you get 1140 and if you add 1140 and 660 you get 1,800
Answer:
Subtract 5x from both sides of the equation.
7y=1−5x
x+4y=−5
Divide each term by 7 and simplify.
y=17−5x/7
x+4y=−5
Subtract x from both sides of the equation.
y=1/7−5x/7
4y=−5−x
y=1/7−5x/7
Divide each term by 4 and simplify.
y=1/7−5x/7
y=−5/4−x/4
y=1/7−5x/7
Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution. (3,−2)
Step-by-step explanation:
