In this question (brainly.com/question/12792658) I derived the Taylor series for 
about 
:
Then the Taylor series for
is obtained by integrating the series above:
We have 
, so 
and so
which converges by the ratio test if the following limit is less than 1:
Like in the linked problem, the limit is 0 so the series for 
converges everywhere.
Answer:
Step-by-step explanation:
Answer:
z - 2*x - 1.5*y = 0 maximize
subject to:
3*x + 5*y ≤ 800
8*x + 3*y ≤ 1200
x, y > 0
Step-by-step explanation:
Formulation:
Kane Manufacturing produce x units of model A (fireplace grates)
and y units of model B
quantity Iron cast lbs labor (min) Profit $
Model A x 3 8 2
Model B y 5 3 1.50
We have 800 lbs of iron cast and 1200 min of labor available
We need to find out how many units x and units y per day to maximiza profit
First constraint Iron cast lbs 800 lbs
3*x + 5*y ≤ 800 3*x + 5*y + s₁ = 800
Second constraint labor 1200 min available
8*x + 3*y ≤ 1200 8*x + 3*y + s₂ = 1200
Objective function
z = 2*x + 1.5*y to maximize z - 2*x - 1.5*y = 0
x > 0 y > 0
The first table is ( to apply simplex method )
z x y s₁ s₂ Cte
1 -2 -1.5 0 0 0
0 3 5 1 0 800
0 8 3 0 1 1200
You have to divide 2029 by 2 to get how many marbles they divided equally. The answer is 2029÷2 = 1014 marbles.
Evaluate t(1),t(2),t(3),t(4)
t(1)=4.5(1)-8=4.5-8=-3.6
t(2)=4.5(2)-8=9-8=1
t(3)=4.5(3)-8=13.5-8=5.5
t(4)=4.5(4)-8=18-8=10
the first 4 terms are
-3.6,1,5.5, 10
