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:
Option C, 262 cm^3
Step-by-step explanation:
<u>Step 1: Substitute 5 for radius and 10 for height</u>
V = 1/3 * pi * r^2 * h
V = 1/3 * pi * (5)^2 * (10)
V = 1/3 * pi * 25 * 10
V = 250pi/3
V = 261.79
Answer: Option C, 262 cm^3
Answer:
Sum
Step-by-step explanation:
Answer:
a. There are 48 angelfish.
b. There are 36 goldfish.
Step-by-step explanation:
the ration of clownfish to angelfish is 5:4 and there are 60 clownfish.
60:? 5x=60 x=12 12(4)=48
60:48 there are 48 angelfish
the ration of angelfish to goldfish is 4:3 and know we know there are 48 angelfish
48:? 4x=48 x=12 12(3)=36
48:36 there are 36 goldfish
Answer:
There are 4 possible ways to place the baseballs into containers.
Step-by-step explanation:
please mark me as brainliest
