Post-Video Questions Preview

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Here are some questions you’ll be asked after you finish watching the videos. Please read through these before watching the videos.

Which notation best represents the right Riemann sum for the function $v(s) = 8.2 \ln (3.8s)$ over the interval $[3,5]$ using $n$ subdivisions of equal length $\Delta s$ ?

$\sum _{k=3}^{5} 8.2 \ln (3.8s_k) \Delta s$
$\sum _{k=3}^{n-1} 8.2 \ln (3.8s_k) \Delta s$
$\sum _{k=1}^{n} 8.2 \ln (3.8s_k) \Delta s$
$\sum _{k=0}^{n} 8.2 \ln (3.8s_k) \Delta s$
$\sum _{k=0}^{n-1} 8.2 \ln (3.8s_k) \Delta s$

Suppose that $f(x) = \frac {x}{2} + 1$ . What is the value of $\sum _{k=1}^3 f(x_k) \Delta x$ over the interval $[2,8]$ using three subdivisions of equal length $\Delta x$ ?

What is the expansion for $\sum _{k=1}^2 2 x_k \Delta x$ over the interval $[5,11]$ using two subdivisions of length $\Delta x = 3$ where $x_0=5$ , and so on?