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2 years ago

Consider the

Mathematics

1 answer:

Cloud [144]2 years ago

3 0

Answer:

the correct answer is the frequency

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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

A company makes two models of television.

VLD [36.1K]

Answer:

16/25

Step-by-step explanation:

length of screen B=44*(5/4)=55cm

and its width=32*(5/4)=40cm

so, screen B had dimensions 55cm by 40 cm

screen A area=44*32 cm sqr

screen B area=55*40 cm sqr

so, model A screen area/model B screen area

=(44*32)/(55*40)

=16/25

5 0

4 years ago

What is the y-intercept of y = - 2x + 6

Scrat [10]

Answer:

Step-by-step explanation:

slope formula y=mx+b

m=slope

b=y-intercept

7 0

3 years ago

Read 2 more answers

The vertices of a triangle are A (2,5) B (1,2) and C (3,1) . Find the coordinates of the image after a dilation with respect to

telo118 [61]

K=2

A'=2(2.5)=(4,10)
B'=2(1,2)=(2,4)
C'=2(3,1)=(6,2)

Translation of 2 units left means change in x

A''=(4-2,10)=(2,10)
B"=(2-2,4)=(0,4)
C"=(6-2,2)=(4,2)

Translation of 1 units up means change in y

A'''=(2,10+1)=(2,11)
B'''=(0,4+1)=(0,5)
C'''=(4,2+1)=(4,3)

5 0

2 years ago

Read 2 more answers

Round 8 5/6 to the nearest whole number

kiruha [24]

Answer:

Step-by-step explanation:

8 5/6

5/6 is close to 1 so it will round up

8+1 = 9

8 5/6 rounds to 9

5 0

3 years ago

Read 2 more answers