Answer:
Part A.
Let f(x) = 0;
suppose x= a+h
such that f(x) =f(a+h) = 0
By second order Taylor approximation, we get
f(a) + hf'±(a) +
f''(a) = 0
± ![\frac{\sqrt[]{(f'(a))^{2}-2f(a)f''(a) } }{f''(a)}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B%5D%7B%28f%27%28a%29%29%5E%7B2%7D-2f%28a%29f%27%27%28a%29%20%7D%20%7D%7Bf%27%27%28a%29%7D)
So, we get the succeeding equation for Newton's method as
± ![\sqrt{f(x_{i})^{2}-2fx_{i}f''x_{i} } ]](https://tex.z-dn.net/?f=%5Csqrt%7Bf%28x_%7Bi%7D%29%5E%7B2%7D-2fx_%7Bi%7Df%27%27x_%7Bi%7D%20%7D%20%5D)
Part B.
It is evident that Newton's method fails in two cases, as:
1. if f''(x) = 0
2. if f'(x)² is less than 2f(x)f''(x)
Part C.
In case
is close to
, the choice that shouldbe made instead of ± in part A is:
f'(x) =
⇔ 
Part D.
As given
=
= h
or h =
- 
We get,
f(a) + hf'(a) +(h²/2)f''(a) = 0
or h² = -hf(a)/f'(a)
Also, (
-
)² = -(
-
)(f(
)/f'(
))
So, f(a) + hf'(a) - (f''(a)/2)(hf(a)/f'(a)) = 0
It becomes h = -f(a)/f'(a) + (h/2)[f''(a)f(a)/(f(a))²]
Also,
=
-f(
)/f'(
) + [(
-
)f''(
)f(
)]/[2(f'(
))²]
They aren’t like terms became 5x^2y has an exponent
We could have the numbers
5x^2 and 5x and they wouldn’t be like terms because one has an exponent
Answer:
A
Step-by-step explanation:
To find the angle inside the triangle (to the right side of 90 degree angle), we first have to find the adjacent angle (below it).
Angle 122 and that adjacent angle is same (parallel lines cut by transversal -- they are corresponding angles).
So that angle is 122.
The inside triangle angle (what we want) is adjacent to 122, so we can write:
Angle + 122 = 180 [straight angle/straight line is 180 degrees]
Solving for that angle, we have:
Angle = 180 - 122 = 58
Now, looking at the triangle, Side C is "opposite" of 58° and side "20" is the side that is "hypotenuse" [side opposite of 90 degree angle is hypotenuse).
<em>Which trig ratio relates "opposite" and "hypotenuse"??</em>
<em>Yes, it is SIN. Thus we can write:</em>
<em>
</em>
<em />
<em>We can now solve for C:</em>
<em>
</em>
<em />
<em>Correct answer is A</em>
SOLUTION:
When looking at this diagram, you can see that CM is equivalent to AM as displayed below:
CM = AM
If:
CM = 7
Then that means that:
AM = 7
Therefore, your answer is:
AM = 7
Answer and Step-by-step explanation:
The computation of annual and quarterly mortality rates per 100,000 population is shown below:-
Quarterly mortality rates are

For the first quarter

= 12 death per 100,000 population
For the second quarter

= 9.5 death per 100,000 population
For the third quarter

= 7.7 death per 100,000 population
For the fourth quarter

= 8.6 death per 100,000 population
Now the annual mortality is


= 38 death per 100,000 population