Post #11

Another week of Calculus gone. During that week we continued to review! For instance we took a quiz and then wrote down five things that we need help with. Mrs. Robinson made us a packet with the top seven types of problems that we needed help on. It's due monday due to some people [NOT ALL] not doing their work in class or asking her to help them. But anyways, I feel that working the problems have helped me a little, however i'm still strugling with Angle of Elevation and the problems that say something like the building is 220 and the initial velocity is -12 ft per second, then an equation is given and it asks you what is the velocity at a certain time..TO ME, that's veryyy confusing!

Wednesday we learned Linearization and the any time we see the word APPROXIMATE we will be using linerarization. For example:
Approximate the tangent line to y=(x)^2 at x=5
that means that dy/dx is 2x
so when we plug in 5 for x we get 2(5) which is 10. 10 is our slope!. Now we will take the original and plug in 5 for x giving us y=(5)^2, so that's y=25.
Since the equation for Linerarization is f(x) = f(c) + f'(c)*(x-c) we will plug in what we have into the equation. we know that f(c)=25...f'(c)=2...and c=5 so when we plug in we get>>>> f(x)=25+2(x-5)

We learned that a differential is when something is solved for dy or dx like:
y=cos(x)---solve for dy
dy/dx = -sin(x)
dy = [(dx)*(-sin(x))]

When we use differentials to approximate there are steps involved:
1. Identify Equation
2. f(x) + f'(x)*dx
3. determine dx
4. determine x
5. Plug in and solve!
For example: (number one on the Approximate part of our wednesday night
homework) to approximate the square root of 99.4 we use the
steps...
~the equation is -- f(x) = the square root of (x)
~the square root of [x] + [(1)/(2 * the square root of [x]) multiplied by (dx)]
~ dx = .4
~ x = 99
~ plug in: [the square root of 99] + [(1) / (2 * the square root of 99) multiplied
by (.4)]
~when solved:....9.96997, the error is 0.0002

I'm still having trouble with the problems on the packet, but other than that I THINK i'm okay!