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:
83
Step-by-step explanation:
Remember that the perimeter of a rectangle is two times the width plus two times the length. In other words:
2W + 2L = P
We know that the perimeter is 290 and the width is 62. We can plug these into the equation and solve for L.
2(62) + 2L = 290
124 + 2L = 290
Subtract 124 from both sides.
2L = 166
Divide both sides by 2.
L = 83
So now we know that the length is 83 feet.
I hope you find my answer and explanation to be helpful. Happy studying.
This is the answer to the question
Answer:
b||c; c||d; b||d
Step-by-step explanation:
Substituting 10 for x, in the angle beside b we have
7(10)-5 = 70-5 = 65
In the angle beside c we have
10(10)+15 = 100+15 = 115
In the angle beside d we have
12(10)-5 = 120-5 = 115
In the angle beside we have
8(10)-25 = 80-25 = 55
The angle beside c has a vertical angle on the other side of c. This angle would be same-side interior angles with the angle beside b; this is because they are inside the block of lines made by b and c and on the same side of a, the transversal. These two angles are supplementary; this is because 65+115 = 180. Since these angles are supplementary, this means that b||c.
The angle beside c and the angle beside d would be alternate interior angles; this is because they are inside the block of lines made by c and d and on opposite sides of the transversal. These two angles are congruent; this means that c||d.
Since b||c and c||d, by the transitive property, b||d.
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