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First, calculate the dot products $y \cdot u = 20$ and $u \cdot u = 5$. The scalar coefficient is $20/5 = 4$.

Conditions: $y = (7,6)$; $u = (2,1)$

First, calculate the dot products $y \cdot u = 20$ and $u \cdot u = 5$. The scalar coefficient is $20/5 = 4$.

Conditions: $y = (7,6)$; $u = (2,1)$

The coefficients are found sequentially by applying the three matching conditions at $x=0$. First, substituting $x=0$ into the polynomial and the function gives $c_0=1$.

Conditions: The approximation is centered at $x=0$.; The target function is $e^x$.; The approximating polynomial is $c_0+c_1x+c_2x^2$.

The coefficients are found sequentially by applying the three matching conditions at $x=0$. First, substituting $x=0$ into the polynomial and the function gives $c_0=1$.

Conditions: The approximation is centered at $x=0$.; The target function is $e^x$.; The approximating polynomial is $c_0+c_1x+c_2x^2$.

Treat the recurring integral as an algebraic variable (e.g., $I$). Move the term containing $I$ from the right-hand side to the left-hand side by adding it to both sides.

Conditions: The integral $I$ appears on both sides of the equation.; The coefficient of $I$ on the right side is $-1$ (or another constant).; Algebraic manipulation is permitted.

Treat the recurring integral as an algebraic variable (e.g., $I$). Move the term containing $I$ from the right-hand side to the left-hand side by adding it to both sides.

Conditions: The integral $I$ appears on both sides of the equation.; The coefficient of $I$ on the right side is $-1$ (or another constant).; Algebraic manipulation is permitted.