Answer:
Σ(-1)^kx^k for k = 0 to n
Step-by-step explanation:
The nth Maclaurin polynomials for f to be
Pn(x) = f(0) + f'(0)x + f''(0)x²/2! + f"'(0)x³/3! +. ......
The given function is.
f(x) = 1/(1+x)
Differentiate four times with respect to x
f(x) = 1/(1+x)
f'(x) = -1/(1+x)²
f''(x) = 2/(1+x)³
f'''(x) = -6/(1+x)⁴
f''''(x) = 24/(1+x)^5
To calculate with a coefficient of 1
f(0) = 1
f'(0) = -1
f''(0) = 2
f'''(0) = -6
f''''(0) = 24
Findinf Pn(x) for n = 0 to 4.
Po(x) = 1
P1(x) = 1 - x
P2(x) = 1 - x + x²
P3(x) = 1 - x+ x² - x³
P4(x) = 1 - x+ x² - x³+ x⁴
Hence, the nth Maclaurin polynomials is
1 - x+ x² - x³+ x⁴ +.......+(-1)^nx^n
= Σ(-1)^kx^k for k = 0 to n
Answer:
100x+120y = z
z= $ 63000
Step-by-step explanation:
Product Welding Assembly Painting Cont. to profit
X 2x hours 3x hours 1xhour = $100x
Y 3y hours 2y hours 1y hour = $120y
<u> </u>
Total hours 1500 hours 1500 hours 550 hours
available
Let X represent product X
Let Y represent Product Y
2x + 3y = 1500
x + y = 550
y= 550-x
2x + 3(550-x) = 1500
2x + 1650- 3x = 1500
150 = x
y = 550-150
y = 400
Objective Function Z = 100x + 120y
Z = 100(150) + 120( 400)
Z = 15000+48000
Z = $63000
<h3>
Answer:</h3>
equations
solution
<h3>
Step-by-step explanation:</h3>
Let "a" and "c" represent the numbers of adult and children's tickets sold, respectively. The problem statement tells us two relationships between these values:
... 20a +10c = 15000 . . . . . . total revenue from ticket sales
... c = 3a . . . . . . . . . . . . . . . . relationship between numbers of tickets sold
Using the expression for c, we can substitute into the first equation to get ...
... 20a +10(3a) = 15000
... 50a = 15000
... a = 15000/50 = 300 . . . . . adult tickets sold
... c = 3·300 = 900 . . . . . children's tickets sold
-3x-2.5=y would be an equivalent to that equation
Answer:
Part 1)
See Below.
Part 2)
Step-by-step explanation:
Part 1)
The linear approximation <em>L</em> for a function <em>f</em> at the point <em>x</em> = <em>a</em> is given by:
We want to verify that the expression:
Is the linear approximation for the function:
At <em>x</em> = 0.
So, find f'(x). We can use the chain rule:
Simplify. Hence:
Then the slope of the linear approximation at <em>x</em> = 0 will be:
And the value of the function at <em>x</em> = 0 is:
Thus, the linear approximation will be:
Hence verified.
Part B)
We want to determine the values of <em>x</em> for which the linear approximation <em>L</em> is accurate to within 0.1.
In other words:
By definition:
Therefore:
We can solve this by using a graphing calculator. Please refer to the graph shown below.
We can see that the inequality is true (i.e. the graph is between <em>y</em> = 0.1 and <em>y</em> = -0.1) for <em>x</em> values between -0.179 and -0.178 as well as -0.010 and 0.012.
In interval notation:
