Linear approximation practice

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Let $g(x) = 2.6 \ln{\left (1.7 x^{2} - 30.6 x + 145.0 \right )}$. Determine a linear approximation $L(x)$ for $g(x)$ that is valid near $x=4.6$. (In all answers, if you round numbers, keep at least four digits.)
$L(x) = $

Using the above linear approximation, estimate the value of $g(4.55)$:

What is the actual value of $g(4.55)$? $g(4.55) = $
Find the linear approximation to the function \[ u( t ) = t^{3} - t \] around $t= 2$.
$L_{ 2 }( t ) =$
Let $h(x)$ be a differentiable function. Given just the information that $h(-8.4) = 1.5$ and $\diff{ h }{x} \big|_{ x = -8.4 } = -9.1$, determine the equation of the tangent line at $x=-8.4$.
$y = $

Using the above tangent line equation, estimate the value of $h(-8.42)$: