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2 years ago

Find the slope from the two points given: (3,9) and (1,8)

Mathematics

1 answer:

Nastasia [14]2 years ago

3 0

Step-by-step explanation:

8-9= -1

1-3= -2

-1/-2= 1

Gradient or Slope= 1

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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

The weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams. What is the weight

SIZIF [17.4K]

800= about 1.76 lbs

700= about 1.54 lbs

(there are about 453.5 grams in a pound

4 0

3 years ago

Read 2 more answers

Castel and Kali are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of

True [87]

Answer:

Plain is $7 and Holiday is $15

Step-by-step explanation:

Castel: 2p + 5h = 89

Kali: 9p + 10h = 213

Double Castel's: 4p + 10h = 178

Subtract fro Kali's 9p + 10h = 213

- 4p + 10h = 178

5p = 35

p = 7 Plain is $7

Substitute 7 into one of the equations and solve for h:

2(7) + 5h = 89

14 + 5h = 89

5h = 75

h = 15 Holiday is $15

6 0

2 years ago

PLS PLS HELP :)) which series of transformations takes the graph of f(x)=2x+3 to the graph of g(x)=-2x+4?

jasenka [17]

B. Reflect the graph about the y-axis and translate one unit up

7 0

3 years ago

A recipe for punch calls for 5 parts grape soda to 2 part seltzer. If hector has 10 cups of of grape soda, how much seltzer does

posledela

Answer:

assuming 10 cups it 10 parts then the answer is 4 cups of seltzer

8 0

2 years ago