Suppose the interval \( [-5,-3] \) is partitioned into \( n=4 \) subintervals. What is the subinterval length \( \Delta x \) ? List the grid points \( x_{0}, x_{1}, x_{2}, x_{3}, x_{4} \) Which points are used for the left right, and midpoint Riemann sums? \( \Delta x=\square \)

b Hence show that \( \int_{2}^{3} \ln y \mathrm{~d} y=\ln \left(\frac{27}{4 \mathrm{e}}\right) \)

A national fast food company has just analyzed the effect of the latest sales promotion. It has determined that the sales decay for its milkshakes is given by \( S=285,000 e^{-0.7 x} \), where \( S \) is the weekly sales and \( x \) is the number of weeks that have passes since the end of the sales promotion. a) Determine the sales 2 weeks after the end of the promotion: Round answer to 2 decimal places. Sales \( =\$ \) b) If no new campaign is started, how many weeks after the end of the promotion will sales drop below 30,000 ? Round answer to 1 decimal place. Num. weeks =

Find the average rate of change of \( h(x)=-2 x^{2}-5 x \) from \( x=-4 \) to \( x=1 \). Simplify your answer as much as possible.

\( : \int _ { - 3 } ( x ^ { 2 } + 7 x - 8 ) d x \)

Find the average rate of change of \( h(x)=-2 x^{2}-5 x \) from \( x=-4 \) to \( x=1 \). Simplify your answer as much as possible.