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2 years ago

Which function does not have a period of 2 pi

Mathematics

1 answer:

fgiga [73]2 years ago

5 0

Answer:

y = tan x

Step-by-step explanation:

y = tan x has a period of pi, not 2pi.

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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

4 years ago

Find the greatest common factor of the terms in the following expression:

ser-zykov [4K]

Answer:

Step-by-step explanation:

32 isn't divisible by any of the other numbers

6 0

3 years ago

Read 2 more answers

The variables y and x have a proportional relationship and y=7 when x=2 what is the value of x when y=21

liubo4ka [24]

Answer:

x=6

Step-by-step explanation:

Since y=7 when x=2, we can from here simplify and see that y=3.5 when x=1. If y=21, then we multiply 7 by 3 which is 21, and since we must keep a proportion, we must multiply 2 by 3 and get 6 as the answer.

4 0

3 years ago

Kaia rewrote the sum 96+12 as 12 (8+1). She used the same method to rewrite the sum 95+15 as 5(19+3). Describe her method and te

djverab [1.8K]

When Kaira wrote 96 +12 as 12(8+1), she "factorized" 12, that is Karira found that 12 is a factor of both 96 and 12.

then she wrote 95+15=5(19+3), that is she factorized 5,

5 is a factor of both 95 and 15 because 95=5* 19 and 15=5*3

To use this method to calculate 38+11 we need 38 and 11 to have some common factor (different from 1),

but 11 is a prime number, that is, it has no factors except 1 and 11. We can only apply the method if 11 is a factor of 38, but it is not.

Answer: The method is called "factorization", and it cannot be applied to calculate 38+11

6 0

4 years ago

A student was asked to use the distributive property to find an expression equivalent to 8(x+6)

leva [86]

8(x+6) = 8x + 48.

8(x+6) is just the factored form.

5 0

3 years ago

Read 2 more answers