The slope of a line is. What is the slope of a line that is parallel to it?

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

An isosceles triangle has an angle that measures 92°. Which other angles could be in that isosceles triangle? Choose all that ap

77julia77 [94]

Answer:

92

Step-by-step explanation:

an iscosolice triagle is a triangle with the sam lenghth on both sides

4 0

3 years ago

Which function has no horizontal asymptote

Nookie1986 [14]

If the polynomial in the numerator is a higher degree than the denominator , there is no horizontal asymptote

7 0

3 years ago

Read 2 more answers

Find the equation of the line parallel to 2y-3x= 4 and passing through the point (6,7)

frutty [35]

Answer:

We have equation of a line:

2y - 3x = 4 => y = (3/2)x + 4

The equation of the line that is parallel to above line and passes through the point (6, 7) would have form y = ax + b, and

a = 3/2

6a + b = 7

=> b = 7 - 6a = 7 - 6 x 3/2 = 7 - 9 = -2

=> The equation of that line: y = (3/2)x - 2

Hope this helps!

:)

7 0

3 years ago

Which expression is equivalent to 1/3p + 15?

SSSSS [86.1K]

Answer:

one over three(p + 45)

one over three(p + 5)

3(p + 45)

3(p + 5)

Step-by-step explanation:

we know that

the expression " one over " is equivalent to

--------> expression A

and

--------> expression B

substitute the expression B in the expression A

-----> one over three

therefore

the answer is the option

one over three(p + 5)

6 0

3 years ago

Read 2 more answers