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3 years ago

What is the degree of g(x) =5x +6x^7 - 8x^3

Mathematics

1 answer:

Ratling [72]3 years ago

5 0

Answer:

...

Step-by-step explanation:

What is the degree of g(x) =5x +6x^7 - 8x^3

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3 years ago

Find the length of the third side. If necessary, write in simplest radical form.

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2 years ago

Solve |10x + 50| = 0.

ryzh [129]

Answer:

a. x=-5

Step-by-step explanation:

|10x + 50| = 0

10x + 50 = 0

10x=-50

x=-5

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3 years ago

(a) Use the power series expansions for ex, sin x, cos x, and geometric series to find the first three nonzero terms in the powe

Fofino [41]

Answer:

a) $\mathbf{4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} ...}$

b) See Below for proper explanation

Step-by-step explanation:

a) The objective here is to Use the power series expansions for ex, sin x, cos x, and geometric series to find the first three nonzero terms in the power series expansion of the given function.

The function is $e^x + 3 \ cos \ x$

The expansion is of $e^x$ is $e^x = 1 + \dfrac{x}{1!}+ \dfrac{x^2}{2!}+ \dfrac{x^3}{3!} + ...$

The expansion of cos x is $cos \ x = 1 - \dfrac{x^2}{2!}+ \dfrac{x^4}{4!}- \dfrac{x^6}{6!}+ ...$

Therefore; $e^x + 3 \ cos \ x = 1 + \dfrac{x}{1!}+ \dfrac{x^2}{2!}+ \dfrac{x^3}{3!} + ... 3[1 - \dfrac{x^2}{2!}+ \dfrac{x^4}{4!}- \dfrac{x^6}{6!}+ ...]$

$e^x + 3 \ cos \ x = 4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} + \dfrac{x^3}{3!}+ ...$

Thus, the first three terms of the above series are:

$\mathbf{4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} ...}$

The series for $e^x + 3 \ cos \ x$ is $\sum \limits^{\infty}_{x=0} \dfrac{x^x}{n!} + 3 \sum \limits^{\infty}_{x=0} ( -1 )^x \dfrac{x^{2x}}{(2n)!}$

let consider the series; $\sum \limits^{\infty}_{x=0} \dfrac{x^x}{n!}$

$|\frac{a_x+1}{a_x}| = | \frac{x^{n+1}}{(n+1)!} * \frac{n!}{x^x}| = |\frac{x}{(n+1)}| \to 0 \ as \ n \to \infty$

Thus it converges for all value of x

Let also consider the series $\sum \limits^{\infty}_{x=0}(-1)^x\dfrac{x^{2n}}{(2n)!}$

It also converges for all values of x

7 0

3 years ago

If Miguel swam 6 lengths of the pool and po swam 3 times as far as Miguel. Lionel swam 1/3 as far as Miguel. What is the equatio

kow [346]

Answer:

Lionel = (1/3)(6 lengths)

Step-by-step explanation:

The problem statement tells us that Lionel swam 1/3 as far as the 6 lengths that Miguel swam. Lionel's distance can be found from the equation ...

Lionel = (1/3)(6 lengths)

3 0

3 years ago

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