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4 years ago

What is the formula of perimeter?

2 answers:

7 0

Add up all of the sides lengths and that is your perimeter... perimeter of a square or rectangle is p(perimeter)=s(side)+s+s+s

cupoosta [38]4 years ago

7 0

The Formula of a rectangle perimeter is the length time the height.

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Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do n

aliya0001 [1]

Answer:

$f(x)=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}$

Step-by-step explanation:

The Maclaurin series of a function f(x) is the Taylor series of the function of the series around zero which is given by

$f(x)=f(0)+f^{\prime}(0)x+f^{\prime \prime}(0)\dfrac{x^2}{2!}+ ...+f^{(n)}(0)\dfrac{x^n}{n!}+...$

We first compute the n-th derivative of $f(x)=\ln(1+2x)$ , note that

$f^{\prime}(x)= 2 \cdot (1+2x)^{-1}\\f^{\prime \prime}(x)= 2^2\cdot (-1) \cdot (1+2x)^{-2}\\f^{\prime \prime}(x)= 2^3\cdot (-1)^2\cdot 2 \cdot (1+2x)^{-3}\\...\\\\f^{n}(x)= 2^n\cdot (-1)^{(n-1)}\cdot (n-1)! \cdot (1+2x)^{-n}\\$

Now, if we compute the n-th derivative at 0 we get

$f(0)=\ln(1+2\cdot 0)=\ln(1)=0\\\\f^{\prime}(0)=2 \cdot 1 =2\\\\f^{(2)}(0)=2^{2}\cdot(-1)\\\\f^{(3)}(0)=2^{3}\cdot (-1)^2\cdot 2\\\\...\\\\f^{(n)}(0)=2^n\cdot(-1)^{(n-1)}\cdot (n-1)!$

and so the Maclaurin series for f(x)=ln(1+2x) is given by

$f(x)=0+2x-2^2\dfrac{x^2}{2!}+2^3\cdot 2! \dfrac{x^3}{3!}+...+(-1)^{(n-1)}(n-1)!\cdot 2^n\dfrac{x^n}{n!}+...\\\\= 0 + 2x -2^2 \dfrac{x^2}{2!}+2^3\dfrac{x^3}{3!}+...+(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}+...\\\\=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^n\dfrac{x^n}{n}$

3 0

3 years ago

Please help its due today!!<br> Solve for h

antiseptic1488 [7]

Answer:

n= v

------------------

1.047198r2

Step-by-step explanation:

Step 1: Flip the equation.

1.047198nr2=v

Step 2: Divide both sides by 1.047198r^2.

1.047198nr2

1.047198r2

8 0

3 years ago

29.87 × 1.089 show work

ankoles [38]

52.22583 srry I couldn’t show work I was In a hurry to go somewhere

8 0

3 years ago

You work part time at taco bell. Your first check is $171. You make an hourly pay of $9.50.

Ostrovityanka [42]

Answer:

No, I'm not old enough to work at taco bell yet

Step-by-step explanation:

7 0

3 years ago

If I had 34 Hershey bars and I ate 2, but I get 69 more and you divide that by 420 what do you get?

Mariulka [41]

Answer:

0.24

Step-by-step explanation:

also i see what you did there

5 0

3 years ago