Month: October 2024

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USA.CsamiGroup.com

• 연변 TM
• 毎日、20통화

CPA.CsamiGroup.com

• 미주 한인 공인회계사
• 미주 주류 사회 CPA
• REMOTE QBO CPA

JinuAcademy.com

• 미주장학재단 version >> 미 주류 진출
• >> Korea.JinuAcademy.com
• >> India.JinuAcademy.com
• >> Japan.JinuAcademy.com

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2037 은퇴 I.II.III.

>> (6)(6)(6) ~2055 “봄 나들이-PhD”

2055, 毎9年 × 5번 도전

>> (9) (9) (9)(9)(9)

• condo nearby utexas (12月~05月)
• – Seattle, WA (05月)
• North Pole, AK duplex (05月~12月)
• – 215 W.7th St. LA, CA 90014 (12月~01月)

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2024~2028

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毎日4時間の学習 @McDonald’s

• 05:00AM~09:00AM
• Safeway
• GREEN – BROWN, free
• Barbershop, Mimi, Costco

USA.CsamiGroup.com

• 연변 TM
• 毎日、20통화

Foothill (AB 540)

• CS
• Economics
• English
• 日本語

CPA.CsamiGroup.com

• BBA, EA QBO CPA
• REMOTE QBO

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2028~2037

JINU 毎9年 1번 도전

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Mathematics MA, IndState

• Mathematics MS., UAF (Sr.Tuition Waiver)
• M.Ed Credential, UAF (Sr.Tuition Waiver)

Statistics MS, UAF (stipend)

• Linguistics BA, UAF
• 日本語 BA, UAF

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毎日4時間の学習 @McDonald’s 生活 ~2037

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“봄 나들이-PhD”

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• (6)(6)(6)

2055(91歳)~

• (9) (9) (9)(9)(9)
• – Computational Science PhDs
• – Forex Algorithmic Trading

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~2037 (73歳)

• 毎日4時間の学習 @McDonald’s
• 05:00AM~09:00AM

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2037~

• “봄 나들이-PhD”
• (6)(6)(6)

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2055 (91歳)~

• (9) (9) (9)(9)(9)

• condo, nice & cozy, nearby
• >> utexas (Sr.Tuition Waiver – 6 units)
• – 12月~05月

• 2793 W.3rd Ave. North Pole, AK 99705 duplex
• >> UAF (Sr.Tuition Waiver)
• – 05月~12月

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2024

2025

..

2027

2028

..

2031

..

2034

..

2037 “毎日4時間の学習 生活”

• (6)(6)(6)
• (9)(9)(9)(9)(9)

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１日、$0.62 >> 총, ~$1,100 (1/2)

• $2,200 >> ~2034 06 毎日4時間の学習 @McDonald’s
• BBA, EA QBO CPA

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~2028 웹 55개 + SSDI EBT Cash Aid

• 毎年、>$2万 저축

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REMOTE QBO

• BBA, EA QBO CPA

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USA.CsamiGroup.com

• 연변 TM
• 毎日、20통화

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CPA.CsamiGroup.com

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JINU “미주장학재단” version

• 5百万、月$.3.50
• >>
• 1百万、月$17.50 (韓日印) “毎9年”

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Newton's method, also known as the Newton-Raphson method, is an iterative numerical technique used to find roots of real-valued functions. The reason it converges to a root can be explained through several key concepts:

### 1. **Function and Derivative**:
Newton's method utilizes both the function $latex f(x)$ and its derivative $latex f'(x)$ to estimate the root. The formula for the iteration is given by:
$latex x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$
This formula gives the next approximation $latex x_{n+1}$ based on the current approximation $latex x_n$.

### 2. **Tangent Line Approximation**:
The essence of Newton's method lies in the geometric interpretation. At each iteration:
- A tangent line is drawn to the function at the point $latex (x_n, f(x_n))$.
- The x-intercept of this tangent line is calculated as the next approximation $latex x_{n+1}$.

The tangent line approximates the function locally, which means if the initial guess $latex x_n$ is close to the actual root, the next guess $latex x_{n+1}$ will typically be closer to the root.

### 3. **Convergence**:
Newton's method exhibits quadratic convergence near the root under certain conditions:
- If $latex x_n$ is sufficiently close to the root $latex r$, then $latex f(x_n)$ will be small, and $latex f'(x_n)$ will be significant.
- The approximation becomes increasingly accurate, and the error decreases rapidly with each iteration.

### 4. **Conditions for Convergence**:
For Newton's method to converge to a root:
- The function $latex f$ must be differentiable in the neighborhood of the root.
- The derivative $latex f'(x)$ should not be zero at the root; otherwise, the method fails as the formula will involve division by zero.
- The initial guess $latex x_0$ should be sufficiently close to the actual root.

### 5. **Mathematical Justification**:
Mathematically, if we denote the root as $latex r$ and assume $latex f(r) = 0$, we can analyze the Taylor series expansion around the root:
$latex f(x_n) = f(r) + f'(r)(x_n - r) + \frac{f''(r)}{2}(x_n - r)^2 + \ldots$
Since $latex f(r) = 0$, this simplifies to:
$latex f(x_n) \approx f'(r)(x_n - r) + \frac{f''(r)}{2}(x_n - r)^2$
The behavior of this expansion shows that as $latex x_n$ approaches $latex r$, the next iteration $latex x_{n+1}$ rapidly approaches the root.

### Conclusion
In summary, Newton's method converges to a root because it uses local linear approximations (tangent lines) to refine guesses iteratively. Given suitable conditions, this method can yield highly accurate approximations to the root with relatively few iterations.

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毎日4時間の学習 @McDonald’s 生活

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USA.CsamiGroup.com

• 연변 TM
• 毎日、20통화

Foothill

• CS >> CS BS MS >> CS MS, utexas
• Economics >> Economics BA MS PhD, utexas
• English >> English BA MA MFA, UAF
• 日本語 >> 日本語 BA PhD, utexas

BBA, EA QBO CPA

• REMOTE QBO

年$78,000 달성 後、毎年、月+$1,000

~2028~2031~2034~2037 은퇴 I.II.III.

JINU 毎9年 × 1번 도전

2037~2064 은퇴 연금 적립

(6)(6)(6) ~2055

JINU 毎9年 × 2번 도전

(9)(9)(9)(9)(9) ~2100

JINU 毎9年 × 5번 도전

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• 2024~2028 “정신병 치료 및 요양”

North Pole Branch Library

>> 2028~ 2031~ 2034~ 2037~

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• (6) 2037~2043″봄 나들이”

Pio Pico

Little Tokyo

LA Central

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• (6) 2043~2049 UMT (stipend)
• (6) 2049~2055″봄 나들이”

(9)(9)(9)(9)(9)

• (9) Computational Science PhD, SDState (stipend)
• – Economics MS, SDState
• (9) CS MS >> Data Science & Engineering PhD, USD (stipend)
• (9) Mathematics PhD, utexas (stipend)
• – CS MS, utexas
• (9) Economics PhD, utexas (stipend)
• (9) 日本語 PhD, utexas (stipend)

condo, nice & cozy, nearby utexas (12月~05月)

• Seattle, WA (05月)

가장 돈 많고 (>”$10B”)

가장 공부 많이 하고 (“PhDs”, utexas)

가장 오래 사는 {韓国人} (>2100)。

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