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:
64 mm³
Step-by-step explanation:
I am assuming there was a photo to go with this problem
However the general formula to find volume is usually V = l×w×h
- It does not matter which measurement is which because they all get multiplied together.
- However assigning a name to each unit of measurement we will denoted the length (l) as 2 mm, the width (w) as 8 mm, and the height (h) as 4 mm
- Plugging these values into the formula we get: V = (2)(8)(4) = 64 mm³
Answer: b. Lin buys a pack of 87 pencils. She gives 39 to her teacher and shared the remaining pencils between herself and 3 friends.
Step-by-step explanation:
Lin buys 87 pencils which is why the entire number line adds up to 87.
She gave 39 of these pencils to her teacher which s why there is a section of the number line that is unlike the rest and is 39 in number.
The rest of the number line is a set of 4 spaces which are equal.
Lin shared the remaining pencils between herself and 3 friends which means she shared the pencils with 4 people. These four equal quantities of pencils are the 4 spaces.
