5. =14
6. =17
hope this helps :)
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:
-86.07
Step-by-step explanation:
Theres a negative 86 and a 7 over 100.
Answer:
The change in the area of the rectangle is 0 square feet
Step-by-step explanation:
To solve this problem we have to calculate the area of the two rectangles that give us
first we have to know the formula to calculate the area of a rectangle
a = area
l = length = 12ft
w = width = 5ft
a = l * w
we replace the known walues
a = 12ft * 5ft
a = 60ft²
we do the same with the other rectangle, but first we have to calculate its sides
w = 5ft - (5ft * 20/100)
w = 5ft - 1ft
w = 4ft
l = 12ft + (12ft * 25/100)
l = 12ft + 3ft
l = 15ft
a2 = 15ft * 4ft
a2 = 60ft²
to calculate the change in the area we subtract (a - a2)
a - a2 =
60ft² - 60ft² = 0ft²
Answer:
Yes it is
Step-by-step explanation:
