Linear approximation practice

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Let $h(x) = \left(- 9.8 x^{2} - 2.8 x + 8\right) e^{- 1.9 x}$. Determine the equation of the tangent line at $x=-0.3$. (In all answers, if you round numbers, keep at least four digits.)
$y = $

Using the above tangent line equation, estimate the value of $h(-0.25)$:

What is the actual value of $h(-0.25)$? $h(-0.25) = $
Find the linear approximation to the function \[ w( t ) = t^{2} \left(t - 1\right) \] around $t= 3$.
$L_{ 3 }( t ) =$
Let $f(x)$ be a differentiable function. Given just the information that $f(5.1) = 1$ and $\diff{ f }{x} \big|_{ x = 5.1 } = 9.2$, determine a linear approximation $L(x)$ for $f(x)$ that is valid near $x=5.1$.
$L(x) = $

Using the above linear approximation, estimate the value of $f(5.15)$: