Use a computer algebra system to find the indicated Taylor polynomials for the function f. Graph the function and the Taylor polynomials. \

$$f(x)=\frac{1}{x^2+1}$$

$n=4, \quad c=0$

Algebra $\triangle A B C$ and $\triangle D E F$ are congruent triangles with $\mathrm{m} \angle A=90^{\circ}, A B=7$, and $D F=24$. Based on the given information, what is the length of $B C$ ?

Simplify the expression

$$Y=A \cdot \bar{B} \cdot \bar{C}+A \cdot \bar{B} \cdot C+\bar{A} \cdot B \cdot C+A \cdot B \cdot C$$

using the boolean algebra.

Use a computer algebra system, if available, to evaluate the expressions that follow. (We will see in the next section how a calculator can be used to evaluate such expressions.)

$$\log _7 45$$

Use a computer algebra system to find the indicated Taylor polynomials for the function f. Graph the function and the Taylor polynomials. \

$$f(x)=\frac{1}{x^2+1}$$

\

$$n=4, \quad c=1$$

Use Maple or another computer algebra system to evaluate and simplify the derivatives of the functions. $\left.\frac{d}{d x} \frac{x \cos (x \sin x)}{x+\cos (x \cos x)}\right|_{x=0}$

In the following exercise, use a computer algebra system to evaluate the iterated integral.

$$\int_0^2 \int_{x^2}^{2 x}\left(x^3+3 y^2\right) d y d x$$

In this exercise, use a computer algebra system to analyze and graph the function. Identify any relative extrema, points of inflection, and asymptotes.

$$f(x)=\frac{20 x}{x^2+1}-\frac{1}{x}$$

The Luncheonette rents a 30-foot by 50-foot area at the Nottingham Mall. The Luncheonette pays $9.20 per square foot per year plus 2% of gross sales. Last year The Luncheonette had$225,000 in gross sales. What was its monthly rent?

Simplify the expression

$$Y=\bar{A} \cdot \bar{B} \cdot \bar{C}+\bar{A} \cdot \bar{B} \cdot C+\bar{A} \cdot B \cdot \bar{C}$$

using the boolean algebra.

Find the integral. Use a computer algebra system to confirm your result.
$\displaystyle\int\left(\tan ^4 t-\sec ^4 t\right) d t$

In the following exercise, use a computer algebra system to graph the surface. (Hint: It may be necessary to solve for $z$ and acquire two equations to graph the surface.)

$$z=\frac{-x}{8+x^2+y^2}$$

Pro forma income statement The marketing department of Metroline Manufacturing estimates that its sales in 2016 will be $\$ 1.5$ million. Interest expense is expected to remain unchanged at $\$ 35,000$, and the firm plans to pay $\$ 70,000$ in cash dividends during 2016. Metroline Manufacturing's income statement for the year ended December 31,2015 , and a breakdown of the firm's cost of goods sold and operating expenses into their fixed and variable components are given below.

a. Use the percent-of-sales method to prepare a pro forma income statement for the year ended December $31,2016$.

Sadie's Car Wash uses the following accounts.

Cash
Supplies
Sadie Berkowitz, Drawing
Sales
Prepaid Insurance Advertising Expense
Miscellaneous Expense
Rent Expense
Accounts Receivable-Zachary's Limos
Accounts Payable-OK Supplies
Accounts Payable-Archer Supplies
Sadie Berkowitz, Capital
Utilities Expense
Repairs Expense 

Transactions:

May  1. Received cash from owner as an investment, $8,000.00. R1.
     2. Paid cash for supplies,$150.00. C1.
     3. Paid cash for rent, $450.00. C2.
     4. Bought supplies on account from Archer Supplies,$850.00. M1.
     5. Paid cash for electric bill, $123.00. C3.
     8. Paid cash on account to Archer Supplies,$500.00. C4.
     8. Received cash from sales, $490.00. TS.
     8. Sold services on account to Zachary's Limos,$225.00. S1.
     9. Paid cash for insurance, $600.00. CS.
    10. Paid cash for repairs,$194.00. C6.
    10. Received cash from sales, $238.00. T10.
    11. Paid cash for miscellaneous expense,$20.00. C7.
    11. Received cash from sales, $315.00. T11.
    12. Received cash from sales,$450.00. T12.
    15. Paid cash to owner as a withdrawal of equity for personal use, $2,000.00. CS.
    15. Received cash from sales,$425.00. T15.
    16. Paid cash for supplies, $550.00. C9.
    17. Received cash on account from Zachary's Limos,$115.00. R2.
    17. Bought supplies on account from OK Supplies, $300.00. M2.
    17. Received cash from sales,$250.00. T17.
    18. Received cash from sales, $400.00. T18.
    19. Received cash from sales,$325.00. T19.
    22. Bought supplies on account from OK Supplies, $30.00. M3.
    22. Received cash from sales,$305.00. T22.
    23. Paid cash for telephone bill, $45.00. C10.
    23. Sold services on account to Zachary's Limos,$291.00. S2.
    24. Paid cash for advertising, $75.00. C11.
    24. Received cash from sales,$150.00. T24.
    25. Received cash from sales, $385.00. T25.
    26. Paid cash for supplies,$45.00. C12.
    26. Received cash from sales, $150.00. T26.
    29. Received cash on account from Zachary's Limos,$175.00. R3.
    31. Paid cash to owner as withdrawal of equity, $2,250.00. C13.
    31. Received cash from sales,$250.00. T31.

Instructions:

5. Prove cash. The beginning cash balance on May 1 is zero. The balance on the next unused check stub is $5,421.00.