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2 years ago

Is 1.41 _ 1.397 equal, less than or more than? which one? please answer this right!!

Mathematics

1 answer:

FromTheMoon [43]2 years ago

8 0

1.41 > 1.397 because yeah

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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

2 years ago

Of the following fractions: 9/19, 5/11, 7/15, and 11/23, which is the largest?

dusya [7]

Answer: 11/23

Step-by-step explanation:

I used my calculator to convert those fractions into decimal form and found the biggest number. It was about 0.4789.

5 0

2 years ago

An item has a listed price of $35 . If the sales tax rate is ,5% how much is the sales tax (in dollars)?

UkoKoshka [18]

Answer:

The sales tax is a 1.75.

Step-by-step explanation:

35 x 0.05 = 1.75

7 0

2 years ago

(2y+3)(3y^2+4y+5) use the chart to multiply the binomial by the trinomial

astra-53 [7]

(2y+3)(3y^2+4y+5)

so u just multiply all the things from different brackets.

2y*3y^2 = 6y^3

2y*4y = 8y^2

2y*2 = 4y

3*3y^2 = 9y^2

3*4y = 12y

3*5 = 15

so 6y^3+8y^2+4y+9y^2+12y+15

thats the answer BUT u need to collect the like terms, otherwise u probably wont get full marks on the question, so:

6y^3+17y^2+16y+15

i hope this helps :)

someone correct me if im wrong

8 0

3 years ago

Tay recorded the number of imported cars that drove by his house during rush hour. He collected data for 5 working days. Taye’s

SCORPION-xisa [38]

Answer: D

Step-by-step explanation:

because

4 0

3 years ago