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oksano4ka [1.4K]
3 years ago
10

Please help! I’ll give brainliest!

Mathematics
1 answer:
Delicious77 [7]3 years ago
3 0

Answer:

to complete ian's the 4th box is 7 and the 5th box is 15

Step-by-step explanation:

orders pairs the 3rd box is 17,3

4th box 55,7

5th box 161,15

i think hope this helps plz brainly if right

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How many nonzero terms of the Maclaurin series for ln(1 x) do you need to use to estimate ln(1.4) to within 0.001?
Vilka [71]

Answer:

The estimate of In(1.4) is the first five non-zero terms.

Step-by-step explanation:

From the given information:

We are to find the estimate of In(1 . 4) within 0.001 by applying the function of the Maclaurin series for f(x) = In (1 + x)

So, by the application of Maclurin Series which can be expressed as:

f(x) = f(0) + \dfrac{xf'(0)}{1!}+ \dfrac{x^2 f"(0)}{2!}+ \dfrac{x^3f'(0)}{3!}+...  \ \ \  \ \ --- (1)

Let examine f(x) = In(1+x), then find its derivatives;

f(x) = In(1+x)          

f'(x) = \dfrac{1}{1+x}

f'(0)   = \dfrac{1}{1+0}=1

f ' ' (x)    = \dfrac{1}{(1+x)^2}

f ' ' (x)   = \dfrac{1}{(1+0)^2}=-1

f '  ' '(x)   = \dfrac{2}{(1+x)^3}

f '  ' '(x)    = \dfrac{2}{(1+0)^3} = 2

f ' '  ' '(x)    = \dfrac{6}{(1+x)^4}

f ' '  ' '(x)   = \dfrac{6}{(1+0)^4}=-6

f ' ' ' ' ' (x)    = \dfrac{24}{(1+x)^5} = 24

f ' ' ' ' ' (x)    = \dfrac{24}{(1+0)^5} = 24

Now, the next process is to substitute the above values back into equation (1)

f(x) = f(0) + \dfrac{xf'(0)}{1!}+ \dfrac{x^2f' \  '(0)}{2!}+\dfrac{x^3f \ '\ '\ '(0)}{3!}+\dfrac{x^4f '\ '\ ' \ ' \(0)}{4!}+\dfrac{x^5f' \ ' \ ' \ ' \ '0)}{5!}+ ...

In(1+x) = o + \dfrac{x(1)}{1!}+ \dfrac{x^2(-1)}{2!}+ \dfrac{x^3(2)}{3!}+ \dfrac{x^4(-6)}{4!}+ \dfrac{x^5(24)}{5!}+ ...

In (1+x) = x - \dfrac{x^2}{2}+\dfrac{x^3}{3}-\dfrac{x^4}{4}+\dfrac{x^5}{5}- \dfrac{x^6}{6}+...

To estimate the value of In(1.4), let's replace x with 0.4

In (1+x) = x - \dfrac{x^2}{2}+\dfrac{x^3}{3}-\dfrac{x^4}{4}+\dfrac{x^5}{5}- \dfrac{x^6}{6}+...

In (1+0.4) = 0.4 - \dfrac{0.4^2}{2}+\dfrac{0.4^3}{3}-\dfrac{0.4^4}{4}+\dfrac{0.4^5}{5}- \dfrac{0.4^6}{6}+...

Therefore, from the above calculations, we will realize that the value of \dfrac{0.4^5}{5}= 0.002048 as well as \dfrac{0.4^6}{6}= 0.00068267 which are less than 0.001

Hence, the estimate of In(1.4) to the term is \dfrac{0.4^5}{5} is said to be enough to justify our claim.

∴

The estimate of In(1.4) is the first five non-zero terms.

8 0
3 years ago
Triangle ABC has vertices at A(-2,-3), B(6,-3), C (-1,5). Answer the following and round your answers to
nirvana33 [79]

Answer:

b.) area of triangle= 1/2 base x height

A to B(base)= 8

height= 8

8 × 8= 64

64÷ 2= 32

area of the triangle= 32

I think this is correct aha

7 0
3 years ago
What is the slope of the line y= -8
Genrish500 [490]
No slope

If you were to graph it the line would be straight across with no rise
7 0
3 years ago
Read 2 more answers
Write in standard form. m is undefined passing through P(-6,-5)
Anna007 [38]

ANSWER: The equation of a line in slope-intercept form looks like the following:   y = mx + b

where m is the slope of the line and b is the y-intercept.

Given any 2 points (x1, y1) and (x2, y2) on a line, the slope (m) = (y2-y1)/(x2-x1).

So, Whenever the slope (m) is undefined it means that when you try to calculate the slope given any 2 points on the line you'll end up with a zero in the denominator, which is undefined. That is, with an undefined slope you end up with a vertical line, which has the equation "x=some number".

 m = (y2-y1)/(x2-x1) = (y2-y1)/0 = undefined. This implies that x2=x1. So x is the same for any value of y on the line, which is why the equation is "x=some number" and the line is vertical. 

So the equation of a line, in slope-intercept form, with an undefined slope (m=undefined) crossing through the point (-3, 5) is:   x= -3 , which is a vertical line. 

Hope this helps you
4 0
3 years ago
Compound inequalities <br> 3&gt;11+k/4&gt;-3
Marat540 [252]

Answer:

−56<k<−32

Step-by-step explanation:

this is the right one

5 0
2 years ago
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