Linear approximation practice

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Find the linear approximation to the function \[ q( x ) = x^{3} - x \] around $x= 3$.
$L_{ 3 }( x ) =$
Let $f(x) = 8.9 e^{- 1.5 x^{2} - 0.4 x - 2}$. Determine a linear approximation $L(x)$ for $f(x)$ that is valid near $x=-1.5$. (In all answers, if you round numbers, keep at least four digits.)
$L(x) = $

Using the above linear approximation, estimate the value of $f(-1.55)$:

What is the actual value of $f(-1.55)$? $f(-1.55) = $
Let $g(x)$ be a differentiable function. Given just the information that $g(-3.9) = -7.2$ and $\diff{ g }{x} \big|_{ x = -3.9 } = 5.3$, determine the equation of the tangent line at $x=-3.9$.
$y = $

Using the above tangent line equation, estimate the value of $g(-3.87)$: