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:
3 ounces.
Step-by-step explanation:
We have been given that Me Zachary brings 264 ounces of water to basketball practice for the players to drink. Mr Zachary divides the water equally among the 9 players. We are asked to find the amount of water that is left over.
To find the amount of water that is left over, we will take out the largest multiple of 9 from 264.
Let us divide 264 by 9.
9) 264(29
<u> 18</u>
84
<u> 81</u>
3
We can see that remainder in 3, therefore, 3 ounces of water will be left over.
Answer:
A
Step-by-step explanation:
for a right angled triangle, the sum of the square of the two sides should be equal to the square of the hypotenuse. If this rule does not hold, the dimensions do not represent the side of a right angled triangle.
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
4² + 10² ≠ 16²
6² + 12² = 13²
7² + 24² = 25²
8² + 15² = 17²
ANSWER
No solution
EXPLANATION
The first equation is
and the second equation is
We equate the two equations to obtain;
This implies that
There is no real number whose square is -1.
Therefore, the equation has no solution.
