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3 years ago

Find the value of n such that (-5)-(-7)>(+9)+(n)

Mathematics

1 answer:

Scorpion4ik [409]3 years ago

4 0

Answer:

The answer is n < -7

Step-by-step explanation:

First, you have to move all the numbers to one side:

(-5) - (-7) > 9 + n

-5 + 7 > 9 + n

9 + n < 2

n < -7

(Hope this can help)

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Consider the function f(x)equalscosine left parenthesis x squared right parenthesis. a. Differentiate the Taylor series about 0

dybincka [34]

I suppose you mean

$f(x)=\cos(x^2)$

Recall that

$\cos x=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{x^{2n}}{(2n)!}$

which converges everywhere. Then by substitution,

$\cos(x^2)=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{(x^2)^{2n}}{(2n)!}=\sum_{n=0}^\infty(-1)^n\frac{x^{4n}}{(2n)!}$

which also converges everywhere (and we can confirm this via the ratio test, for instance).

a. Differentiating the Taylor series gives

$f'(x)=\displaystyle4\sum_{n=1}^\infty(-1)^n\frac{nx^{4n-1}}{(2n)!}$

(starting at $n=1$ because the summand is 0 when $n=0$ )

b. Naturally, the differentiated series represents

$f'(x)=-2x\sin(x^2)$

To see this, recalling the series for $\sin x$ , we know

$\sin(x^2)=\displaystyle\sum_{n=0}^\infty(-1)^{n-1}\frac{x^{4n+2}}{(2n+1)!}$

Multiplying by $-2x$ gives

$-x\sin(x^2)=\displaystyle2x\sum_{n=0}^\infty(-1)^n\frac{x^{4n}}{(2n+1)!}$

and from here,

$-2x\sin(x^2)=\displaystyle 2x\sum_{n=0}^\infty(-1)^n\frac{2nx^{4n}}{(2n)(2n+1)!}$

$-2x\sin(x^2)=\displaystyle 4x\sum_{n=0}^\infty(-1)^n\frac{nx^{4n}}{(2n)!}=f'(x)$

c. This series also converges everywhere. By the ratio test, the series converges if

$\displaystyle\lim_{n\to\infty}\left|\frac{(-1)^{n+1}\frac{(n+1)x^{4(n+1)}}{(2(n+1))!}}{(-1)^n\frac{nx^{4n}}{(2n)!}}\right|=|x|\lim_{n\to\infty}\frac{\frac{n+1}{(2n+2)!}}{\frac n{(2n)!}}=|x|\lim_{n\to\infty}\frac{n+1}{n(2n+2)(2n+1)}$

The limit is 0, so any choice of $x$ satisfies the convergence condition.

3 0

3 years ago

if Pedro were 7.5 cm taller he would be twice as tall as Ian. Ian is 74.25 cm tall so how tall is Pedro?

Afina-wow [57]

Pedro is 141 cm tall.

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3 years ago

5a+2=6-7a please help me fellows

stira [4]

6 0

3 years ago

Connie and ron walked to a dock at 2 miles per hour, jumped in a boat and motired to dillons at 7 miles per hour. If the total d

ExtremeBDS [4]

Answer:

10.5 miles

Step-by-step explanation:

Let b represent the distance traveled by boat. The relation between speed, distance, and time is ...

time = distance / speed

We are told the total time and the total distance so we have ...

b/7 + (14-b)/2 = 3.25

2b +7·14 -7·b = 14·3.25 . . . multiply by 14

3.75·14 = 5b . . . . . . . . . . . .add 5b-14·3.25

b = 10.5 . . . . . . . . . . . . . . . divide by 5

They traveled 10.5 miles by boat.

_____

<em>Check</em>

10.5/7 +3.5/2 = 1.5 +1.75 = 3.25 . . . . the answer checks OK

They spent 1.75 hours walking 3.5 miles to the dock and 1.5 hours traveling 10.5 miles by boat.

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3 years ago

What is 2.1 times 10 to the power four

lutik1710 [3]

2.1 x 10 to the power of 4.
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3 years ago

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