Find the linear approximation at $x=0$ to show that the following commonly used approximations are valid for "small" $x$. Compare the approximate and exact values for $x=0.01, x=0.1$ and $x=1$. $$ e^{x} \approx 1+x $$
Added by Sara E.
Step 1
This is given by the equation of the tangent line to the graph of $y=e^x$ at $x=0$. The slope of this tangent line is the derivative of $e^x$ evaluated at $x=0$, which is $e^0=1$. The $y$-intercept of the tangent line is the value of $e^x$ at $x=0$, which is Show more…
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