Linear approximation practice

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Find the linear approximation to the function \[ v( t ) = \left(t - 6\right)^{3} + 3 \] around $t= 7$.
$L_{ 7 }( t ) =$
Let $g(x)$ be a differentiable function. Given just the information that $g(8.2) = 6.3$ and $g'(8.2) = 3.5$, determine the equation of the tangent line at $x=8.2$.
$y = $

Using the above tangent line equation, estimate the value of $g(8.25)$:
Let $h(x) = \left(5.2 x^{2} - 4.8 x - 5.2\right) e^{1.7 x}$. Determine a linear approximation $L(x)$ for $h(x)$ that is valid near $x=-0.1$. (In all answers, if you round numbers, keep at least four digits.)
$L(x) = $

Using the above linear approximation, estimate the value of $h(-0.06)$:

What is the actual value of $h(-0.06)$? $h(-0.06) = $