no school tomorrow! yessssss :) haha, so this week mon-fri, we did the same thing. every day. review ap test questions, took a couple practice ap tests in 5th hour, went over them. pretty much everything we've learned this year, we went over. haha
Related Rates:
1. Identify all variables and equations
2. Identify what you are looking for
3. Make a sketch and label
4. Write an equation involving your variables
5. Take the derivative with respect to time
6. Substitute in derivative and solve.
Example:
Air is being pumped into a spherical balloon at a rate of 4.5 cubic ft/min. Find the rate of change of the radius when the radius is 2 ft.
1. r=2ft; dv/dt = 4.5 ft^3/min
2. NEED TO FIND dr/dt.
3. Volume of sphere: v=4/3 pi r^3
4. derivative: dv/dt = 4 pi r^2 dr/dt
5. Plug in: 4.5 = 4pi(2)^2 dr/dt
6. 4.5=16 pi dr/dt
dr/dt = 9/32 pi ft/min
i finally am starting to understand all the lram rram tram mram stuff, but i couldn't explain it. i have to see it. AP tests seem to have a lot of repeating questions. i get e integration too!
u is always whatever e is raised to(the exponent)
du is always the derivative.
simply use substitution and solve.
i also understand disks and washers.. but unfortunately i did forget the formulas. haha
what i mainly have problems with is word problems.. which is pretty much everything! so, idk what to do. i guess i just need practice. someone please refresh my memory with disk and washers area and volume formulas for both!
Subscribe to:
Post Comments (Atom)
i know rolles therom... the functin must be ontinuous on the interval given, it has to be differentiable and f(a)=f(b)
ReplyDeletethen take the derivative and set it equal to zero to solve for either x or c.
volume by disks-solid object
ReplyDeleteformula: pi S[r(x)]^2dx
volume by washers-a hole in it (means it is bounded by two graphs)
formula: pi S top^2-bottom^2 dx
washers- square the top minus the square the bottom. and then take the intergral
ReplyDeleteFor the word problems, just read it, and while doing so, write down anything you think might be relevant and if said put which derivative it falls under.
ReplyDeletevolume by disks-solid object
ReplyDeleteformula: pi S[r(x)]^2dx
volume by washers-a hole in it
formula: pi S top^2-bottom^2 dx
volume by disks:
ReplyDeletethe formula is pi times the integral of the [function given] squared times dx. so just solve it by taking the integral of it and then pluging in the numbers they give you. just like before you'll have two numbers so whatever the answer is for the top one will be first and then you subtract the answer you get for the bottom one. then graph
volume by washers:
the formla is pie times the integral of the [top function] squared minus the [bottom function] squared times dx. so to do this, if you don't have the in between number you have to set the functions equal, but if you do, then it's worked the same way as above. square the formula's that were given and simplify. then take the integral of it and plug in the numbers they give you or you found by setting the formulas equal to each other and then solve like any other one by subracting them. then graph.
The formula for volume by disks is piS[R(x)]^2 dx.
ReplyDeleteThe formula for volume by washers is piStop^2 - bottom^2 dx
If the graph is not given, graph it in your calculator to see which one is on top.