Linear approximation practice

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Let $h(x)$ be a differentiable function. Given just the information that $h(0.1) = 0.3$ and $h'(0.1) = -7.7$, determine a linear approximation $L(x)$ for $h(x)$ that is valid near $x=0.1$.
$L(x) = $

Using the above linear approximation, estimate the value of $h(0.11)$:
Find the linear approximation to the function \[ f( s ) = e^{- s + 2} \left(s - 6\right) \] around $s= 2$.
$L( s ) =$
Let $f(x) = \left(- x^{2} - 9.6 x + 6.2\right) \ln{\left (x \right )}$. 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 $f(1.49)$:

What is the actual value of $f(1.49)$? $f(1.49) = $