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.
The equation for a circle is
(x-h)² + (y-k)² = r²
h = your given x
y = your given k
Let's plug everything in!
(x - 5) ² + (y - (-1)) ² = 12²
Your final equation is
(x - 5) ² + (y + 1) ² = 144
<em>Hope I helped! Comment or message me if you have any questions :) </em>
Answer:
b
Step-by-step explanation:
if you subtract 5x then you will get y=-10-5x
Let 
= amount of salt (in pounds) in the tank at time 
(in minutes). Then 
.
Salt flows in at a rate
and flows out at a rate
where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.
Then the net rate of salt flow is given by the differential equation
which I'll solve with the integrating factor method.
Integrate both sides. By the fundamental theorem of calculus,
After 1 hour = 60 minutes, the tank will contain
pounds of salt.
Answer:
since her score was -12 from being perfect
if she had scored 12 more points her score would have been perfect .
that is difference between her score and the perfect score o each quiz was <u>12</u>
