Linear approximation practice

Name:
Group members:

Section:

Find the linear approximation to the function \[ u( x ) = x^{3} - x \] around $x= 3$.
$L_{ 3 }( x ) =$
Let $h(x)$ be a differentiable function. Given just the information that $h(4.5) = 8.1$ and $\diff{ h }{x} \big|_{ x = 4.5 } = -7.7$, determine the equation of the tangent line at $x=4.5$.
$y = $

Using the above tangent line equation, estimate the value of $h(4.51)$:
Let $h(x) = - 6.7 e^{1.5 x^{2} + 3.5 x + 1}$. Determine the equation of the tangent line at $x=2$. (In all answers, if you round numbers, keep at least four digits.)
$y = $

Using the above tangent line equation, estimate the value of $h(1.98)$:

What is the actual value of $h(1.98)$? $h(1.98) = $