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Alinara [238K]
3 years ago
13

Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that

Rn(x) → 0.] f(x) = 8x − 3x3, a = −2 [infinity] f n(−2) n! (x + 2)n n = 0 = 8 − 28(x + 2) + 18(x + 2)2 − 3(x + 2)3 [infinity] f n(−2) n! (x + 2)n n = 0 = 8 − 28(x + 2) + 3(x + 2)2 − 18(x + 2)3 [infinity] f n(−2) n! (x + 2)n n = 0 = 8 + 28(x + 2) + 18(x + 2)2 + 3(x + 2)3 [infinity] f n(−2) n! (x + 2)n n = 0 = 8 − 18(x + 2) + 28(x + 2)2 − 3(x + 2)3
Mathematics
1 answer:
kherson [118]3 years ago
5 0

Answer:

The answer is

f(x) = {\displaystyle  8 + \frac{-28}{1}(x+2)+\frac{-36}{2!}(x+2)^2 + \frac{-18}{3!}(x+2)^2 }

Step-by-step explanation:

Remember that Taylor says that

f(x) = {\displaystyle \sum\limits_{k=0}^{\infty} \frac{f^{(k)}(a) }{k!}(x-a)^k }

For this case

f^{(0)} (-2) = 8(-2)-3(-2)^3 = 8\\f^{(1)} (-2) = 8-3(3)(-2)^2 = -28\\f^{(2)} (-2) = -3(3)2(-2) = -36\\f^{(2)} (-2) = -3(3)2 = -18

f(x) = {\displaystyle  8 + \frac{-28}{1}(x+2)+\frac{-36}{2!}(x+2)^2 + \frac{-18}{3!}(x+2)^2 }

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Solve the following expression when f = 2 &amp; s = 8<br><br> s ÷ (2f)
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answer is 2

Step-by-step explanation:

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3 years ago
A pentagonal prism has a height of 9 feet, and each base edge is 3 feet. Find the volume. Round your answer to the nearest hundr
OLga [1]

Height of the pentagon = 9 ft

Edge of base = 3 ft

area of pentagon = \frac{s^{2}n}{4 tan\left ( \frac{180}{n} \right )}

s is the length of any side = 3

n is the number of sides = 5

tan is the tangent function calculated in degrees

\\ \\\\area of pentagon = \frac{3^{2}(5)}{4 tan\left ( \frac{180}{5} \right )}\\\\\\area of pentagon = \frac{9(5)}{4 tan\left ( 36 \right )}\\\\area of pentagon = \frac{45}{4  ( 0.7265 )}\\\\area of pentagon = \frac{45}{2.906}\\\\area of pentagon = 15.4852

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Volume of the pentagon = 15.4852 (9)

Volume of the pentagon = 139.366

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5 0
3 years ago
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Which of the following best describes the total area of the exterior surface of a solid figure?
Free_Kalibri [48]
The answer is D, Surface area
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3 years ago
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It’s my last question :(
jenyasd209 [6]

Answer:

Perimeter =  28·√2 + 24 feet

Step-by-step explanation:

The dimensions of the initial sheet of plywood are;

The length of the sheet of plywood = 25 ft.

The width of the sheet of plywood = 14 ft.

The shape cut from each corner of the sheet of plywood  = A right triangle

The leg length of each of the cut out right triangles = 7 ft.

The number of leg lengths of the right triangle cut from the length side of the initial sheet of plywood = 2

The length of the parallel sides of the remaining hexagonal piece of plywood = Initial length of the plywood - 2 × The leg length of the cut out right triangle

∴ The length of the parallel sides of the remaining hexagonal piece of plywood = 26 ft. - 2 × 7 ft.  = 12 ft.

The other side length of the remaining hexagonal piece of plywood = The hypotenuse side of the cut out right triangle

The hypotenuse side of the cut out right triangle = √((7 ft.)² + (7 ft.)²) = 7·√2 ft.

∴ The other side length of the remaining hexagonal piece of plywood = 7·√2

The number of side lengths in the remaining hexagonal piece of plywood = 4

The perimeter of the remaining hexagonal piece of plywood = 2 × The length of the parallel sides + 4 × The other side lengths

∴ The perimeter of the remaining hexagonal piece of plywood = 2 × 12 ft. + 4 × 7·√2 = (28·√2 + 24) ft.

The perimeter of the remaining hexagonal piece of plywood = (28·√2 + 24) feet

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3 years ago
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