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3 years ago

Will give brainliest!!!!

Mathematics

1 answer:

ExtremeBDS [4]3 years ago

6 0

Answer: a reflection across the y axis

Step-by-step explanation:

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Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for each function.

Lunna [17]

Answer:

The first three nonzero terms in the Maclaurin series is

$\mathbf{ 5e^{-x^2} cos (4x) }= \mathbf{ 5 ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }$

Step-by-step explanation:

GIven that:

$f(x) = 5e^{-x^2} cos (4x)$

The Maclaurin series of cos x can be expressed as :

$\mathtt{cos \ x = \sum \limits ^{\infty}_{n =0} (-1)^n \dfrac{x^{2n}}{2!} = 1 - \dfrac{x^2}{2!}+\dfrac{x^4}{4!}-\dfrac{x^6}{6!}+... \ \ \ (1)}$

$\mathtt{e^{-2^x} = \sum \limits^{\infty}_{n=0} \ \dfrac{(-x^2)^n}{n!} = \sum \limits ^{\infty}_{n=0} (-1)^n \ \dfrac{x^{2n} }{x!} = 1 -x^2+ \dfrac{x^4}{2!} -\dfrac{x^6}{3!}+... \ \ \ (2)}$

From equation(1), substituting x with (4x), Then:

$\mathtt{cos (4x) = 1 - \dfrac{(4x)^2}{2!}+ \dfrac{(4x)^4}{4!}- \dfrac{(4x)^6}{6!}+...}$

The first three terms of cos (4x) is:

$\mathtt{cos (4x) = 1 - \dfrac{(4x)^2}{2!}+ \dfrac{(4x)^4}{4!}-...}$

$\mathtt{cos (4x) = 1 - \dfrac{16x^2}{2}+ \dfrac{256x^4}{24}-...}$

$\mathtt{cos (4x) = 1 - 8x^2+ \dfrac{32x^4}{3}-... \ \ \ (3)}$

Multiplying equation (2) with (3); we have :

$\mathtt{ e^{-x^2} cos (4x) = ( 1- x^2 + \dfrac{x^4}{2!} ) \times ( 1 - 8x^2 + \dfrac{32 \ x^4}{3} ) }$

$\mathtt{ e^{-x^2} cos (4x) = ( 1+ (-8-1)x^2 + (\dfrac{32}{3} + \dfrac{1}{2}+8)x^4 + ...) }$

$\mathtt{ e^{-x^2} cos (4x) = ( 1 -9x^2 + (\dfrac{64+3+48}{6})x^4+ ...) }$

$\mathtt{ e^{-x^2} cos (4x) = ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }$

Finally , multiplying 5 with $\mathtt{ e^{-x^2} cos (4x) }$ ; we have:

The first three nonzero terms in the Maclaurin series is

$\mathbf{ 5e^{-x^2} cos (4x) }= \mathbf{ 5 ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }$

7 0

3 years ago

Please help!! I need this answer please!! i will mark brainliest if correct thanks!!!

adell [148]

9514 1404 393

Answer:

(0.5, -2.5)

Step-by-step explanation:

Each of the coordinates of B(1, -5) is multiplied by the scale factor, 0.5:

B' = (0.5·1, 0.5·(-5)) = (0.5, -2.5)

The coordinates of B' are (0.5, -2.5).

3 0

3 years ago

Mark is a coin collector. At the first store he went to, he bought 3 sets of 4 coins. At the second store, he bought 5 sets of 3

kramer

Answer: 2 coins

3 • 4 + 5 • 3 - 5 - 8

6 0

4 years ago

Simplify (5+11i) - (16-4i) +9i.

lisabon 2012 [21]

Answer:

5+11i-16-4i+9i

5-16+11i-4i+9i

-11+7i+9i

-11+16i

Step-by-step explanation:

First, get the like terms together. Then add or subtract until its simplified. Simplified is -11+16i.

6 0

3 years ago

Read 2 more answers

BRAINILEST!!!!Karim builds a wooden table.

Liula [17]

To solve this problem you must apply the proccedure shown below:

1. The area of the rectangle is:

$A=WL$

Where $W$ is the width and $L$ is the length.

2. Based on the data given, solve for the width and then substitute the values of the length and the values of the area. Therefore, you have:

$W=\frac{A}{L} \\ W=27 inches$

The answer is the second option:

$27 inches$

8 0

4 years ago

Read 2 more answers

Will give brainliest!!!!​

Will give brainliest!!!!