This week that we call the 11th week of blogging; we didn’t really learn anything new we just mostly reviewed old stuff such an angle of elevation and related rates which I still have a lot of trouble with just like everything else. But the new thing we did learn I actually understand I was surprised at first. We learned linearization at the end of the week and I know how to do it. I think it’s called linearization. We also got this big packet that I really don’t know how to do that’s do Monday so im nervous about that.
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. you can only have an unknown so a secondary equation may be given.5. take the derivative with respect to time.6. substitute in derivative and solve.an example problem would be
the variable x and y are differentiable functions of t and are related by the equation
y=2x^3-x+4 when x=2 dx/dt=1. find dy/dt when x=2.dy/dt=?x=2 dx/dt=-1 y=2x^3-x+4dy/dt=6x^2dx/dt-dx/dtdy/dt=6(2)^2(-1)+(1)dy/dt=-23
Now for everything I don’t know which is a lot my biggest problem is still trying to find the equation for the problem and im bad at related rates angle of inclination and optimization so any help that you can give and im also bad at that packet so if anyone wants to help me out be my guess.
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Related Rates steps:
ReplyDelete1. Identify 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 derivative with respect to time
6. Substitue in derivative and solve
Example: A sperical balloon is inflated with gas at the rate of 200 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radium is 70cm?
Given: dv/dt= 200; r=70
Equation: v=4/3pir^3
Looking for: dr/dt
Take derivative of equation with respect to time: dv/dt=4pir^2dr/dt
Plug in: 200=4pi(70)^2 (dr/dt)
Solve: dr/dt= 200/19600pi
which equals: 1/98pi
For problems with related rates, the best thing to do is write down all that you are given, and when they say something is changing at a certain rate, it will always be d something over dt.
ReplyDeleteThen you have to identify an equation to plug everything into such as area, volume, etc.
then once everything is plugged in take the derivative and solve for the unknown variable.
Hope this helps!
for Related Rates:
ReplyDelete1: identify all variables in equations
2: identify what you are looking for
3: sketch and lebel
4: write an equation involving your variables. (you can only have one unkown so a secondary equation may be given)
5: take the derivative with respect to time.
6: substitute derivative and solve.
Example: the variables x and y are functions of t and related by the equation y=2x^3-x+4 when x=2, dy/dt=-1. Find dy/dt when x=2
alright, so you put down the equation, y=2x^3-x+4.
Then you take the derivative of that, so you get dy/dt=6x^2(dx/dt)-(dx/dt)
then you plug in to find that dy/dt=6(2)^2(-1)-(-1)
and that is further simplified to, dy/dt=-23.