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:
So if y=-4x+2 was changed to y=-4x+5, then the y-intercept would increase by 3.
The y-intercept was (0,2) then it becomes (0,5) in the new line.
Step-by-step explanation:
The slope-intercept form a line is y=mx+b where m is the slope and the y-intercept is b.
Both of these equations given are in this form.
y=-4x+2 when compared to y=mx+b you see that m=-4 and b=2.
Since b=2 then the y-intercept is 2.
y=-4x+5 when compared to y=mx+b you see that m=-4 and b=5.
Since b=5 then the y-intercept is 5.
So if y=-4x+2 was changed to y=-4x+5, then the y-intercept would increase by 3.
First combine like terms on each side so
8x = -7x
then move -7x
so x=0
Answer:
1. 24,000,000, i believe you divide, 300,000/80.
2. 4.065 seconds, i also believe you divide 5000m/1230.
