Linearization, Mean Value Theorem and Euler's Method

Using the derivative

Tangent line at x = a

L (x) = f (a) + f^{'} (a) (x - a)

Mean value theorem

f^{'} (c) = \frac{f (b) - f (a)}{b - a}

for some c between a and b

Euler's method

y_{n + 1} = y_{n} + h \cdot f (x_{n}, y_{n})

for dy/dx = f(x, y), step size h

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