QuestionC) Calculate $L_{3}$ and $R_{3}$ for $f(x)=\frac{12}{x}$ on $[2,5]$

Studdy Solution
Calculate the right Riemann sum $R_3$:
The right endpoints of the subintervals are $x_1 = 3$, $x_2 = 4$, and $x_3 = 5$.
\[ R_3 = \Delta x \left[ f(x_1) + f(x_2) + f(x_3) \right] $
Substitute the function values:
$R_3 = 1 \left[ \frac{12}{3} + \frac{12}{4} + \frac{12}{5} \right]$
Simplify:
$R_3 = 1 \left[ 4 + 3 + 2.4 \right] = 9.4$
The values of $L_3$ and $R_3$ are:
$$L_3 = 13$$ $$R_3 = 9.4$$