Consider the initial-value problem y = y, y(0) = 1,and let yn denote the approximation

Chapter 8, Problem 25

(choose chapter or problem)

Consider the initial-value problem $y^{\prime}=y, y(0)=1$, and let $y_{n}$ denote the approximation of y(1) using Euler’s Method with n steps.

(a) What would you conjecture is the exact value of $\lim _{n \rightarrow \infty} Y_{n}$? Explain your reasoning.

(b) Find an explicit formula for yn and use it to verify your conjecture in part (a).

Equation Transcription:

${y}^{'}\ =\ y,\ y(0)\ =\ 1$

${y}_{n}$

$\lim\limits_{{n} \rightarrow {\infty{}}}\ {Y}_{n}$

Text Transcription:

y' = y, y(0) = 1

y_n

lim_n rightarrow + infinity Y_n

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