Answer:
Step-by-step explanation:
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so answer for (A is 1)
Answer for (B is 100)
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Answer:
(n^3 + 4 n + 4487)/(n + 1)
Step-by-step explanation:
Simplify the following:
(n^3 + 4 n - 2 + 67^2)/(n + 1)
| | 6 | 7
× | | 6 | 7
| 4 | 6 | 9
4 | 0 | 2 | 0
4 | 4 | 8 | 9:
(n^3 + 4 n - 2 + 4489)/(n + 1)
Grouping like terms, n^3 + 4 n - 2 + 4489 = n^3 + 4 n + (4489 - 2):
(n^3 + 4 n + (4489 - 2))/(n + 1)
4489 - 2 = 4487:
Answer: (n^3 + 4 n + 4487)/(n + 1)
Step-by-step explanation:
Consider LHS
Apply quotient identies
Multiply the fraction and sine.
Make cos x a fraction with cos x as it denominator.
so
Pythagorean Identity tells us sin squared and cos squared equals 1 so
Apply reciprocal identity.
We want to solve the Initial Value Problem y' = y + 4xy, with y(0) = 1.
To use Euler's method, define
y(i+1) = y(i) + hy'(i), for i=0,1,2, ...,
where
h = 0.1, the step size.,
x(i) = i*h
1st step.
y(0) = 1 (given) and x(0) = 0.
y(1) ≡ y(0.1) = y(0) + h*[4*x(0)*y(0)] = 1
2nd step.
x(1) = 0.1
y(2) ≡ y(0.2) = y(1) + h*[4*x(1)*y(1)] = 1 + 0.1*(4*0.1*1) = 1.04
3rd step.
x(2) = 0.2
y(3) ≡ y(0.3) = y(2) + h*[4*x(2)*y(2)] = 1.04 + 0.1*(4*0.2*1.04) = 1.1232
4th step.
x(3) = 0.3
y(4) ≡ y(0.4) = y(3) + h*[4*x(3)*y(3)] = 1.1232 + 0.1*(4*0.3*1.1232) = 1.258
5th step.
x(4) = 0.4
y(5) ≡ y(0.5) = y(4) + h*[4*x(4)*y(4)] = 1.258 + 0.1*(4*0.4*1.258) = 1.4593
Answer: y(0.5) = 1.4593
