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34kurt
3 years ago
14

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) = 4 x , a = −2
Mathematics
1 answer:
Nutka1998 [239]3 years ago
3 0

Answer:

4x

Step-by-step explanation:

The Taylor series of a function f(x) about a value x = a is given by f(x) = f(a) + f'(a)(x - a)/1! + f''(a)(x - a)²/2! + f'''(a)(x - a)³/3! + ... where the terms in f prime f'(a) represent the derivatives of x valued at a.

For the given function, f(x) = 4x and a = -2

So, f(a) = f(-2) = 4(-2) = -8

f'(a) = f'(-2) = 4

All the higher derivatives of f(x) evaluated at a are equal to zero. That is f''(a) = f'"(a) =...= 0

Substituting the values of a = -2, f(a) = f(-2) = -8 and f'(-2) = 4 into the Taylor series, we have

f(x) = f(-2) + f'(-2)(x - (-2))/1! + f''(-2)(x - (-2))²/2! + f'''(-2)(x - (-2))³/3! +...

= -8 + 4(x + 2)/1! + (0)(x + 2)²/2! + (0)(x + 2)³/3! +...

= -8 + 4(x + 2) + 0 + 0

= -8 + 4x + 8

= 4x

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olganol [36]
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Let's call the smaller angle x and the larger y.
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x + 3x = 90
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4 0
3 years ago
Which of the following graphs shows the preimage P(x)=x^2 and the image I(x)=P(1/3x)?
Ksju [112]

Answer:

The picture with the widest graph in red

Step-by-step explanation:

The graph P(x) is the parent graph for all quadratic functions. It has a vertex of (0,0) and has the following points:

x      f(x)

-2      4

-1       1

0       0

1         1

2       4

The image of l(x) = P(1/3x) changes the points of the function to

x      f(x)

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-1/3        1/9

0       0

1/3        1/9

2/3       4/9

This makes the graph much wider. The graph with the widest red graph is the graph.

7 0
3 years ago
Read 2 more answers
Step by step explanation need it
nasty-shy [4]

Answer:

8/17

Step-by-step explanation:

The sine of an angle is defined as the opposite side to the reference angle divided by the hypotenuse.

The side opposite the angle is always the side not connected to the reference angle. In this case the opposite side = ZY

The hypotenuse = XZ

Sin(X) = ZY/XZ

Sin(X) = 1634 = 8 / 17

4 0
2 years ago
HELP!! URGENT!! GIVING AWAY 50 POINTS to correct answer!!
NNADVOKAT [17]

The figure seems like its a parallelogram.

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Opposite sides are equal and
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7 0
3 years ago
Read 2 more answers
Can someone answer all these for me pls
Tems11 [23]
Okay
1 yes and yes
2 yes and no
3 no and yes
4 0
3 years ago
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