Alrighty then, I learned related rates this week because I wasn't at school the week before, and I also learned linearization.
Related Rates:
1: 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.
Linearization:
f(x)=f(c)+f'(c)(x-c)
example: Approximate the tangent line to y=x^2 at x=1
you find all the different values: dy/dx=2x dy/dx=2 y=(1)^2=1
then you plug into the formula to get: f(x)=1+2(x-1)
example 2: use differentials to approximate: sq root(16.5)
steps:
1: identify an equation--- f(x)=sq root(x)
2:f(x)+f;(x)dx--- sqrt(x)+ (1/(2sqrt(x)))(dx)
3:determine dx-- .5
4:determine x--- 16
5:plug in--- sqrt(16)+(1/2sqrt(16))(.5)= 4.0625
error= .0005
so I did learn how to do that stuff, and did pretty well on that quiz that we had earlier in the week. I am actually quite happy because I have been starting to pass my quizzes, so I am glad we started this new stuff because I am actually understanding it quite well.
One thing I do not understand is angle of elevation, I don't really have any notes on it, just an example problem, so I have not been able to really learn it just by looking at that. If anyone has any advice, it would be greatly appreciated.
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Angle of elevation problems can sometimes change...
ReplyDeleteYou either use tan theta = x/y and you have one of those variables constant or you can use something like sin = y/hyp or cos = x/hyp
Okay for angle of elevation problems you can use tan theta= x/y or you have constants then use sin= y/hyp or cos=x/hyp. hope this helps
ReplyDeleteyou can use SOHCAHTOA to get the angle and take the derivative.
ReplyDeleteAngle of elevation problems are not always the same.
ReplyDeleteYou can use something like sin = y/hypotenuse or cos= x/hypotenuse depending what is given.
or if given one of the variables you can use tan theta = x/y
this probably doesn't make that much sense but that's what i got :)
for angle of elevation problems, you are going to have to look for an angle to solve your problems or you may have to look for a leg. You can use the tan(x/y), sin(y/hypotenuse) or cos(x/hypotenuse)functions. I hope this helps!
ReplyDeleteiknow to use sohcahtoa and take the der.
ReplyDelete