Is y=7x-3 proportional or non-proportional?
2 answers:
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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
±
So, we get the succeeding equation for Newton's method as
±
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]
Answer:
Step-by-step explanation:
First we need to compute the side length as a function of h
So x be the side length of the right isosceles triangle, in Pythagorean formula we have
The cost for the legs is
The cost for the hypotenuse is
So the total cost in term of h is