Leasing Workbook: Fill & Download for Free

This is an interesting question.I am currently writing an integration workbook for students between AP Calculus AB and senior year of undergraduate college, so I feel like I can provide some insights. When I start thinking of answers, I start thinking of answers to, “what is the hardest integral technique to master?” So, for new calculus students, I would say the following techniques are fair game:I have included some example problems from my workbook - some are common and some were formulated backwards by yours truly.U-substitution (definite & indefinite - changing bounds) [math]\displaystyle\int \sqrt{4-\sqrt{x}} dx[/math]Trigonometric substitutions [math]\displaystyle\int e^{4x}\sqrt{1+e^{2x}} dx[/math]Using a right triangle for trig substitutions involving inverse trig functions *this is an awesome one that I created - leave me a comment if you think you have the answer* [math]\displaystyle\int_0^1 \frac{arctan(x)}{tan(arccos(\frac{x^{2}}{\sqrt{2x^{4}+2x^{2}+1}}))} dx[/math]Graphing integrand and using geometric arguments [math]\displaystyle\int_{-3}^{3} \sqrt{9-x^{2}} dx[/math]Logarithmic and exponential properties → special substitutions [math]\displaystyle\int \frac{1}{\sqrt{e^{2x}-1}} dx[/math] *at lease two ways to solve this one*Integration by parts type 1 [math]\displaystyle\int_{0}^{1} xsin(x) dx[/math]Integration by parts type 2 (formula involving original integral) [math]\displaystyle\int (sec(x))^{3} dx[/math] *I love these*Rational functions - completing the square [math]\displaystyle\int \frac{1}{x^{2}+14x+50} dx[/math]Rational functions - long division [math]\displaystyle\int \frac{x^{3}}{x^{2}-1} dx[/math]Rational functions - standard Partial Fraction Decomposition (PFD) [math]\displaystyle\int \frac{3x+5}{(x-3)(2x+1)} dx[/math]Rational functions - repeated factor PFD [math]\displaystyle\int \frac{3x+1}{(x-1)^{2}(x+2)} dx[/math]Rational functions - quadratic factor PFD [math]\displaystyle\int \frac{5x}{(x^{2}+x+1)(x-2)} dx[/math]Rational functions - higher order factors & repeated factors PFD [math]\displaystyle\int \frac{5x}{(x^{2}+x+1)(x-2)^{2}} dx[/math]Honorable mentions, but likely considered “too hard” for the scope of this question:Improper integralsIntegrals requiring the use of Taylor Series & integrating term by term[math]Sin(x)+Cos(x)[/math] can be written as a single [math]ASin(h+x)[/math] or [math]ACos(h+x)[/math] where [math]A[/math] is a different amplitude and [math]h[/math] is a phase shift [math]\displaystyle\int_0^{\frac{\pi}{2}} \frac{2(sin(x))^{2}cos(x)+2sin(x)(cos(x))^{2}}{\sqrt{2}cos(x-\frac{\pi}{4})} dx[/math]Half & double angle formulas + reduction formulasYou can see my answer involving some next level techniques: HERE.See my answer on partial fractions: HERE.After this point, it would be hard to argue that the following techniques are still “introductory” level.Obviously, the hardest integrals involve using many of these techniques in successive order and only in that exact order. With regards to the question, with any of these flavors, it is somewhat difficult to find a challenging problem that only uses a single technique.In my opinion, for most students, as a single technique, repeated root partial fraction decomposition integrals lead to the highest number or arithmetic mistakes while also seldomly being fully understood by the brighter students. One could argue, however, that any of the PFD problems are not a single technique because they almost always result in solving integrals that require the use of the arctangent derivative, u-substitution, and or logarithmic properties.EDIT: Following clue** #3 requires the use of a triangle to simplify the expression inside tan(), then simplify the expression for tan() itself, make a u-sub, and finally use I.B.P.**

So are the people living in the house, making payments? Do you get a check from them? Are they destructive? Is a church making the payment?Give them a 30 Day, Notice Of Inspection. Have a Lease Agreement made out for 1 year. Go to Staples to get a workbook with legal forms, that you can scan and copy. You can change wording on the forms when they are copied, to suit your needs.Then go inspect the premises. See what needs to be addressed. Have them sign a new lease, and take a picture with your phone of ID or Drivers License. Know who is there. They don’t have an ID? No lease? Start the eviction process. It will take 3 months.When you enter the home for inspection, don’t be cordial. Be as close to business as you can. No smiles. No gestures of friendship. And take VIDEO, with your phone. Look at bathrooms, look at cabinets, look at doorways. Really inspect what you can. Look at the STOVE AND OVEN, if it is your stove. Document as much in the video as you can. At the beginning of your video, state who you are, and the date of this video log, the address you are visiting.

There are, I believe, three things that affect the cost of a car lease:The new price of the carThe expected residual value of that car in 24 or 36 months (term of the lease) with “those miles on the car” (what the lease allows for mileage)The interest rate on the money.Typically, when you lease a new car from a new car dealer, you are not leasing it from the dealer, but from a financial institution that owns the vehicle and that is typically related to the company (in the USA) that manufacturers or imports that vehicle.For example, when I lease an Audi A4, I am not leasing from the dealer, but from “Audi Financial”.You can negotiate the new price of the car.You can show the Percentage of value that the car should have after the term of the lease (percentage of sale price).You can “negotiate” the interest rate if you know what you doing.Be “educated” before you enter the dealership to “negotiate” and have two things that you want:Maximum number of dollars you are willing to pay to start the lease (reduce the amount that is “financed” through the lease interest rate)The maximum monthly amount you can afford to pay for a lease (and remember that your state’s sales tax is charged on the monthly lease payment)Make a Excel workbook and do your homework in Advance of contacting the dealerships and you will be fine.Good luck.