post 27

Okay, after having a good mardi gras break i'm going to have to do this blog, so for this particular one i am going to go over related rates and linearization.

Related Rates:

1: identify all variables in equations
2: identify what you are looking for
3: sketch and label
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

since we have to post something that we also have trouble with in our blogs, i'm going to go ahead and say that i could use some refreshing on angle of elevation, whoever wants to help with that can do that..