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.
5 1/4 - 2 2/3
first you find the LCM, so u can make both fractions have a like denominator. I'm thinking the LCM is 12, so:
(5 3/12) - (2 8/12)
= 63/12 - 32/12
=31/12
= 2 and 7/12
5 1/4 - 2 2/3 = 2 7/12
Answer:
6x - 11 feet
Step-by-step explanation:
Dale is standing (2x + 7) feet height from the base of the tower.
And the tower is given to be (8x - 4)feet tall.
We have to find the distance between Dale and the top of the tower.
Now, the distance between dale and the top of the tower = height of the tower - height of Dale = (8x - 4) - (2x + 7) = (6x - 11) feet. (Answer)
Answer:
4
Step-by-step explanation:
y = 4*x
y = 4*1.5 = 6
y = 4*2.25 = 9
y = 4* 3.25 = 13
Answer:
17% , 15% , 6% , 10% , 40% , 6%
Step-by-step explanation:
You're going to have to divide the number of people who voted for those positions by the total number of people.
Adapting = 9 / 52 = 17%
Other = 8 / 52 = 15%
Yes = 3 / 52 = 6%
No = 5 / 52 = 10%
Absolutely = 21 / 52 = 40%
Maybe = 3 / 52 = 6%