Calculus Answers

Calculus
Find -3x
Using first principles

Fernando wants to start an annual scholarship program. He wants to have three five thousand dollar scholarships and one ten thousand dollar scholarship per year. The bank is offering Certificates of Deposit with an annual simple interest rate of 4% per year. How much money would Fernando need to invest in CD's to be able to pay for the scholarships with interest earned each year.

The regular price of a ticket on a FLuffy Kitty Cruise Lines is $990 per person. Each cruise ship can hold at most 150 passengers. They are running a promotion this month for each confirmed reservation everyone gets $5 off their total ticket price. For example if 10 people make reservations the discounted ticket price will be $950 each. How many reservations should Fluffy Kitty Cruise Lines take to maximize their profit?

From the following information pertaining to M/s ABC & Co. Ltd., prepare its trading, profit & Loss A/c for the year ending 31st March 2012 and summarized Balance Sheet as on that date.
Current ratio - 2.5
Quick Ratio - 1.3
Proprietary ratio - 0.06
Gross Profit to sales - 10%
Debtors Velocity - 40 days
Sales - 273000
Working capital - 120000
Bank overdraft - 215000
Share Capital - 250000
Closing Stock is 10% more than opening stock
Net profit 10% of proprietary fund.

4. Test the significance of variation of the retail prices of the commodity in three principle cities; Bombay, Kolkata and Delhi. The four shops were chosen at random in each city and prices observed in rupees were as follows
Bombay 16 8 12 14
Kolkata 14 10 10 6
Delhi 4 10 8 8

Obtain the Fourier series for the following periodic function which has a period of 2pi
f(x)=(pi^2)-(x^2) for -pi<x<pi

A demand curve has equation q=100-5p, where p is price in dollars. A $2 tax is imposed on consumers. Find the equation of the new demand curve. Sketch both curves.

Is the force field defined by F =(3x^2yz-3y ) i+(x^3z-3x ) ˆj+(x^3y+2 )kˆ
conservative? If
so, find the scalar potential associated with F.

Find the limit if it exist. If it does not exist explain why.

Two questions
1
Limit of cot x
As x approaches pi
and
2
Limit of (2 - absolute(-x))
As x approaches 3

I have the answers from the book but dont understand what process I need to get there. #1 doesnt exist but my in my calc it looks like its 18.something. #2 I substitued in the 3 but get -1 but it aso doesnt exist somehow.

Thanks

Dear Expert Hi,Please tell me about the Null Matrix.Is it in Echelon form or not?Explain your answer.
best wishes