Washer method Let R be the region bounded by the following curves. Use the washer method to find the volume of the solid generated when R is revolved about the x-axis.
$y=2 x, y=16 x^{1 / 4}$

Use the Newton-Raphson method to find an approximate solution of the given equation in the given interval. Use the method until successive approximations obtained by calculator are identical.

$$x^2+4 x^6=2 ;[0,1]$$

In the following problem, determine approximate values of the solution $x=\phi(t), y=\psi(t)$ of the given initial value problem at t = 0.2, 0.4, 0.6, 0.8, and 1.0. Compare the results obtained by different methods and different step sizes.

$x^{\prime}=x(x+y+1)$, $y^{\prime}=y(x+y)$, x(0) = 1, y(0) = 1

Use the Runge-Kutta method with h = 0.1.

Ramirez Co. decides at the beginning of 2010 to adopt the FIFO method of inventory valuation. Ramirez had used the LIFO method for financial reporting since its inception on January 1, 2008, and had maintained records adequate to apply the FIFO method retrospectively. Ramirez concluded that FIFO is the preferable inventory method because it reflects the current cost of inventory on the balance sheet. The table presents the effects of the change in accounting principle on inventory and cost of goods sold.

$$\begin{array}{|c|c|c|c|c|} \hline \text { Date } & \text { LIFO Method } & \text { FIFO Method } & \text { LIFO Method } & \text { FIFO Method } \\ \hline \text { January } 1,2008 & \$ 0 & \$ 0 & \$ 0 & \$ \quad 0 \\ \hline \text { December 31, } 2008 & 100 & 80 & 800 & 820 \\ \hline \text { December 31, } 2009 & 200 & 240 & 1,000 & 940 \\ \hline \text { December 31, } 2010 & 320 & 390 & 1,130 & 1,100 \\ \hline \end{array}$$

Other information:

1. For each year presented, sales are $4,000 and operating expenses are$1,000.
2. Ramirez provides two years of financial statements. Earnings per share information is not required.

(b) Prepare income statements reflecting the retrospective application of the accounting change from the LIFO method to the FIFO method for 2010 and 2009.

Use the Newton-Raphson method to find an approximate solution of the given equation in the given interval. Use the method until successive approximations obtained by calculator are identical.

$$\tan x=x ;(\pi / 2,3 \pi / 2)$$

Explain motility within the small intestine.

Let R be the region bounded by the following curves. Let S be the solid generated when R is revolved about the given axis. If possible, find the volume of S by both the disk/washer and shell methods. Check that your results agree and state which method is easier to apply. y=x,

$$y=x^{1/3}$$

in the first quadrant; revolved about the x-axis

The small intestine has three parts which are ________, ________, and _________.

Define entrepreneur, startup, small business incubator, inventory, receipts.

Solve the equation for exact solution in the interval $\left[0^{\circ}, 360^{\circ}\right)$. Use either an algebraic method or a graphical method.

$$\sin \theta+\cos \theta=1$$

Solve the equation for exact solution in the interval $\left[0^{\circ}, 360^{\circ}\right)$. Use either an algebraic method or a graphical method.

$\sec \theta-\tan \theta=1$

In the following problem, determine approximate values of the solution $x=\phi(t), y=\psi(t)$ of the given initial value problem at t = 0.2, 0.4, 0.6, 0.8, and 1.0. Compare the results obtained by different methods and different step sizes.

$x^{\prime}=t x+y+1$, $y^{\prime}=x$, x(0) = 1, y(0) = 1

Use the Euler method with h = 0.1.

Identify and describe the anatomy of the small intestine.

Consider executing the following code on the pipelined datapath of earlier Figure:

add $2,$3, $1
sub$4, $3,$5
add $5,$3, $7
add$7, $6,$1
add $8,$2, $6

At the end of the fifth cycle of execution, which registers are being read and which register will be written?