Falling action of a good man is hard to find

Integrate 1 - x / x(x2 + 1) d x by partial fractions.

solniwko [45]

Answer:

$log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x$

Step-by-step explanation:

step 1:- by using partial fractions

$[tex]\frac{1-x}{x(x^{2}+1) } =\frac{A(x^{2}+1)+(Bx+C)(x }{x(x^{2}+1) }$ ......(1)

step 2:-

solving on both sides

$1-x=A(x^{2} +1)+(Bx+C)x......(2)$

substitute x =0 value in equation (2)

1=A(1)+0

A=1

comparing x^2 co-efficient on both sides (in equation 2)

0 = A+B

0 = 1+B

B=-1

comparing x co-efficient on both sides (in equation 2)

-1 = C

step 3:-

substitute A,B,C values in equation (1)

now

$\\\int\limits^ {} \, \frac{1-x}{x(x^{2}+1) } d x =\int\limits^ {} \frac{1}{x} d x +\int\limits^ {} \frac{-x}{x^{2}+1 } d x -\int\limits \frac{1}{x^{2}+1 } d x$

by using integration formulas

i) by using $\int\limits \frac{1}{x} d x =log x+c........(a)\\\int\limits \frac{f^{1}(x) }{f(x)} d x= log(f(x)+c\\$ .....(b)

$\int\limits tan^{-1}x dx =\frac{1}{1+x^{2} } +C$ .....(c)

step 4:-

by using above integration formulas (a,b,and c)

we get answer is

$log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x$

6 0

3 years ago

3×-18=42 Solve for x!

Keith_Richards [23]

3x - 18 = 42
3x = 42 + 18
3x = 60
x = 60/3
x = 20

7 0

3 years ago

What is typically used to quantitatively compare the effectiveness of layouts? A. trial and error B. load-distance model C. expo

Andre45 [30]

Answer:

B. load-distance model

Step-by-step explanation:

A. trial and error

Trial and error is "a fundamental method of problem solving. It is characterised by repeated, varied attempts which are continued until success". But this method is not the best in order to compare effectiveness of layouts

B. load-distance model

The load-distance method is a "mathematical model used to evaluate locations based on proximity factors. The objective is to select a location that minimizes the total weighted loads moving into and out of the facility. The distance between two points is expressed by assigning the points to grid coordinates on a map". And that's the correct option since we are trying to measure the effectiveness of layouts quantitatively.

C. exponential smoothing

This is "a rule of thumb technique for smoothing time series data using the exponential window function". Wheighting observations using the exponential function. But this is a techinique used to smooth s time series not to compare effectiveness of layouts.

D.process control charts

The Control Chart is a "graph used to study how a process changes over time with data plotted in time order". But we don't want to see how the process changes the objective is quantitatively compare the effectiveness of layouts, and this one is not the best option for this.

E. mean absolute deviation (MAD)

The median absolute deviation(MAD) is "a robust measure of how spread out a set of data is. The variance and standard deviation are also measures of spread, but they are more affected by extremely high or extremely low values and non normality". But again is just a measure of spread and not allow to compare effectiveness of layouts.

8 0

3 years ago

Ok her it is need help

Furkat [3]

Answer:

..........

Step-by-step explanation:

5 0

3 years ago

There is a vendor at a carnival selling bags of cotton candy. Each bag of cotton candy has the same cost. She starts each day wi

umka21 [38]

Answer: