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Semenov [28]
3 years ago
12

Assume that f(x)=ln(1+x) is the given function and that Pn represents the nth Taylor Polynomial centered at x=0. Find the least

integer n for which Pn(0.2) approximates ln(1.2) to within 0.01.
Mathematics
1 answer:
WINSTONCH [101]3 years ago
7 0

Answer:

the least integer for n is 2

Step-by-step explanation:

We are given;

f(x) = ln(1+x)

centered at x=0

Pn(0.2)

Error < 0.01

We will use the format;

[[Max(f^(n+1) (c))]/(n + 1)!] × 0.2^(n+1) < 0.01

So;

f(x) = ln(1+x)

First derivative: f'(x) = 1/(x + 1) < 0! = 1

2nd derivative: f"(x) = -1/(x + 1)² < 1! = 1

3rd derivative: f"'(x) = 2/(x + 1)³ < 2! = 2

4th derivative: f""(x) = -6/(x + 1)⁴ < 3! = 6

This follows that;

Max|f^(n+1) (c)| < n!

Thus, error is;

(n!/(n + 1)!) × 0.2^(n + 1) < 0.01

This gives;

(1/(n + 1)) × 0.2^(n + 1) < 0.01

Let's try n = 1

(1/(1 + 1)) × 0.2^(1 + 1) = 0.02

This is greater than 0.01 and so it will not work.

Let's try n = 2

(1/(2 + 1)) × 0.2^(2 + 1) = 0.00267

This is less than 0.01.

So,the least integer for n is 2

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Step-by-step explanation:

736 / 365 = 2R6

So even if the first 365 students all have different birthdays, and the next 365 students also all have different birthdays, then there are 2 students for every birthday.  The last 6 students therefore share a birthday with at least 2 other students.  So there are at least 3 students who share a birthday.

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3 years ago
What ratios are equivalent<br> to 3/5
barxatty [35]
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3 years ago
Solve x - 3 &lt; -1. Graph the solution.
LuckyWell [14K]

Answer: x < 2

Explanation: To solve for <em>x</em> in this inequality, our goal is the same as it would be if this were an equation, to get <em>x</em> by itself on one side.

Since 3 is being subtracted from <em>x</em>, we add 3

to both sides of the inequality to get <em>x < 2</em>.

Before we graph, write your answer in set notation.

We can write this as {x: x < 2}.

It's important to understand what this means.

This means that any number less than 2 is a solution to this inequality.

I have graphed the inequality for you below.

Start with an open dot on +2.

We use an open dot because +2 is not included as a solution.

Then draw an arrow going to the left.

3 0
3 years ago
In pensacola in june, high tide was at noon. the water level at high tide was 12 feet and 2 feet at low tide. assuming the next
castortr0y [4]

An equation for water level in june for pensacola as a function of time (t) is f(t) = 5 cos pi/6 t + 7.

Which equation of cos show period amplitude ?

The equation given below show aplitude and period

y = A cos bx + c

where A = amplitude,

b = 2 pi/Period,

Period = 12 hrs,

c = midline,

x = t and y = f(t)

We have to find the amplitude

<h3>What is the formula for the amplitude?</h3>

A = 1/2 (Xmax - Xmin)

12 - 2 / 2 = 10/2 = 5

b = 2 pi / 12 = pi/6

c = 1/2 (Xmax + Xmin)

12+2/2 = 7

Therefore, the an equation for water level in june for pensacola as a function of time (t)

f(t) = 5 cos pi/6 t + 7

To learn more about the function of time visit:

brainly.com/question/24872445

3 0
2 years ago
Which value of c would make the following express completely factored? 8x+cy
Artist 52 [7]
The answer is B, 7.

\sf 8x+2y

We can factor a 2 out of this: \sf 2(4x+y)

\boxed{\sf 8x+7y}

We can't factor anything.

\sf 8x+12y

We can factor a 4 out of this: \sf 4(2x+3y)

\sf 8x+16y

We can factor an 8 out of this: \sf 8(x+2y)

So your answer is B, 7.
6 0
3 years ago
Read 2 more answers
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