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Please answer this question to the best of your ability. You are welcome to re-watch parts of any of the videos to help you. Note: in these questions, the left hand side of the first interval is denoted by $x_0$ .

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 $\Delta s$ ?

$\sum _{k=3}^{5} 8.2 \ln (3.8s_k) \Delta s$ $\sum _{k=3}^{n-1} 8.2 \ln (3.8s_k) \Delta s$ $\sum _{k=1}^{n} 8.2 \ln (3.8s_k) \Delta s$ $\sum _{k=0}^{n} 8.2 \ln (3.8s_k) \Delta s$ $\sum _{k=0}^{n-1} 8.2 \ln (3.8s_k) \Delta s$ None of the above

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 $\Delta x$ ?

15 18 19 21 24 28 None of the above

Which of the following is the correct 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?

$2 \times 5 \times 3 + 2 \times 8 \times 3$ $2 \times 8 \times 3 + 2 \times 11 \times 3$ $2 \times 5 \times 3 + 2 \times 8 \times 3 + 2 \times 11 \times 3$ $2 \times 5 \times 3 + 2 \times 6 \times 3 + 2 \times 7 \times 3 + 2 \times 9 \times 3 + 2 \times 10 \times 3 + 2 \times 11 \times 3$