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3 years ago

Consider the function represented by the graph. What is the domain of this function?

Mathematics

1 answer:

stiv31 [10]3 years ago

8 0

Answer:

I think it is B but i'm not 100% sure.

Step-by-step explanation:

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y′′ −y = 0, x0 = 0 Seek power series solutions of the given differential equation about the given point x 0; find the recurrence

sukhopar [10]

Let

$\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = a_0 + a_1x + a_2x^2 + \cdots$

Differentiating twice gives

$\displaystyle y'(x) = \sum_{n=1}^\infty na_nx^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n = a_1 + 2a_2x + 3a_3x^2 + \cdots$

$\displaystyle y''(x) = \sum_{n=2}^\infty n (n-1) a_nx^{n-2} = \sum_{n=0}^\infty (n+2) (n+1) a_{n+2} x^n$

When x = 0, we observe that y(0) = a₀ and y'(0) = a₁ can act as initial conditions.

Substitute these into the given differential equation:

$\displaystyle \sum_{n=0}^\infty (n+2)(n+1) a_{n+2} x^n - \sum_{n=0}^\infty a_nx^n = 0$

$\displaystyle \sum_{n=0}^\infty \bigg((n+2)(n+1) a_{n+2} - a_n\bigg) x^n = 0$

Then the coefficients in the power series solution are governed by the recurrence relation,

$\begin{cases}a_0 = y(0) \\ a_1 = y'(0) \\\\ a_{n+2} = \dfrac{a_n}{(n+2)(n+1)} & \text{for }n\ge0\end{cases}$

Since the n-th coefficient depends on the (n - 2)-th coefficient, we split n into two cases.

• If n is even, then n = 2k for some integer k ≥ 0. Then

$k=0 \implies n=0 \implies a_0 = a_0$

$k=1 \implies n=2 \implies a_2 = \dfrac{a_0}{2\cdot1}$

$k=2 \implies n=4 \implies a_4 = \dfrac{a_2}{4\cdot3} = \dfrac{a_0}{4\cdot3\cdot2\cdot1}$

$k=3 \implies n=6 \implies a_6 = \dfrac{a_4}{6\cdot5} = \dfrac{a_0}{6\cdot5\cdot4\cdot3\cdot2\cdot1}$

It should be easy enough to see that

$a_{n=2k} = \dfrac{a_0}{(2k)!}$

• If n is odd, then n = 2k + 1 for some k ≥ 0. Then

$k = 0 \implies n=1 \implies a_1 = a_1$

$k = 1 \implies n=3 \implies a_3 = \dfrac{a_1}{3\cdot2}$

$k = 2 \implies n=5 \implies a_5 = \dfrac{a_3}{5\cdot4} = \dfrac{a_1}{5\cdot4\cdot3\cdot2}$

$k=3 \implies n=7 \implies a_7=\dfrac{a_5}{7\cdot6} = \dfrac{a_1}{7\cdot6\cdot5\cdot4\cdot3\cdot2}$

so that

$a_{n=2k+1} = \dfrac{a_1}{(2k+1)!}$

So, the overall series solution is

$\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = \sum_{k=0}^\infty \left(a_{2k}x^{2k} + a_{2k+1}x^{2k+1}\right)$

$\boxed{\displaystyle y(x) = a_0 \sum_{k=0}^\infty \frac{x^{2k}}{(2k)!} + a_1 \sum_{k=0}^\infty \frac{x^{2k+1}}{(2k+1)!}}$

4 0

3 years ago

Pls help i will give brainliest

Novosadov [1.4K]

<h3>Answer: -a > -b</h3>

Explanation:

Let's go over an example.

We'll have a = 1 and b = 7 which makes a < b true. Feel free to pick your own favorite pair of numbers such that b is larger than 'a'.

The corresponding opposites are: -a = -1 and -b = -7

The relationship flips because the opposites of each number are flipped. So instead of saying -a < -b, we have -a > -b

Sure enough, -1 > -7 is a true statement. Use a number line to see this. I recommend a vertical number line.

In short, going from a < b to -a > -b means we flip the signs of each term, and we flip the inequality sign as well.

4 0

3 years ago

Help me plzzzzzzzzzzzzzzzz i have untel 5

mojhsa [17]

Answer:

First image:

27 / 9 = 3

2.7 / 0.9 = 3

33.3/0.09 = 3

Second image:

168 / 2 = 84

16.8 / 0.2 = 84

1.68 / 0.02 = 84

7 0

3 years ago

Read 2 more answers

A bag with 8 marbles has 8 yellow marbles. A marble is chosen from the bag at random. What is the probability that it is yellow?

konstantin123 [22]

Answer: 1

Step-by-step explanation:

8 yellow / 8 total = 8/8 = 1

8 0

3 years ago

Bob says that when he multiplies (x+3) (x-3) he gets x^2-6x-9 is he correct explain

almond37 [142]

(x+3)(x-3)
x*x=x^2
x*-3=-3x
3*x=3x
3*-3=-9

where’s where he most likely messed up
x^2-3x+3x-9

the correct answer is x^-9

5 0

3 years ago