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.
Slope = Y2-Y1/X2-X1 = 7-(-3)/3-(-2)= 10/5 = 2
Answer:
136 cm²
Step-by-step explanation:
Surface area = 2(lw+wh+hl)
l = 7
w = 2
h = 6
so,
2(7×2+2×6+7×6)
= 136 cm²
The question is incorrect
the correct question is
A local citizen wants to fence a rectangular community garden. The length of the garden should be at least 110 ft,and the distance around should be no more than 380 ft. Write a system of inequality that model the possible dimensions of he garden. Graph the system to show all possible solutionslet
x---------------> t<span>he length of the garden
</span>y---------------> the wide of the garden
we know that
x>=110
2x+2y <=380---------------> x+y <= 190
Part A) <span>Write a system of inequality that model the possible dimensions of he garden
</span>
the answer part A) is
x>=110
x+y <= 190
Part B) <span>Graph the system to show all possible solutions
using a graph tool
see the attached figure
the solution is the triangle show in the figure
</span><span>the possible solutions of y (wide) would be between 0 and 80 ft
</span>the possible solutions of x (length) would be between 110 ft and 190 ft
First factor -12m^n - 49mn - 44n^2 to get -(4n+3m)(11n + 4m) then the equation would be:
-(3m + 4n)(4m + 11n) / (-3m - 4n)
Then, cancel out the like terms and the final answer would be
4m + 11n