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3 years ago

Find the linear approximation of f(x)=lnx at x=1 and use it to estimate ln(1.38).

1 answer:

5 0

$\bf f(x)=y=ln(x)\qquad 
\begin{cases}
x=1\\
y=ln(1)\to y=0
\end{cases}\\\\
-----------------------------\\\\
\left. \cfrac{dy}{dx}=\cfrac{1}{x} \right|_{x=1}\implies 1\impliedby m
\\\\\\
\textit{now, we know that }
\begin{cases}
x=1\\
y=0\\
m=1
\end{cases}\implies y-0=1(x-1)\implies y=x-1$

now, you're asked to use it when ln(1.38), which is just another way of saying x = 1.38

so set x = 1.38 and see what "y" is

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Compare this to the actual root of $f(x)$ , which is approximately <u>1.76929</u>2354, matching up to the first 5 digits after the decimal place.

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