Question

Will pay $10 through paypal for the correct answer. See attached file in the comments.

Answer 1

the file isnt attached. :o

Answer 2

I think I know how to do two of the questions. But I'm really not sure. And I don't want to find out after it's been graded...

Answer 3

umm, sorry i can't help u with these.. but i know people who can help.. but u have to wait for a couple of hours for them..
this site is free to use, people help u for free, no dont use the paypal thing. LOL

try asking, satellite, myininya, zarkon, a.msitre etc.

Answer 4

Damn, okay... And those people aren't on at the moment?

Thanks for trying.

Answer 5

No they aren't.. but they will be in some hours...

Answer 6

i know that nCr formula.. but i used that in binomial expansion!

Answer 7

Hoodrych, do you know how to do a linear approximation?

Answer 8

Yeah, somewhat. We've learned it. That's what it is over.

Answer 9

What are you using to graph? (calculator, software, etc?)

Answer 10

I shouldn't need one..

Answer 11

Let's say they wanted you to approximate \(f(x) = \sin(x)\) using a linear \(L(x)\) and quadratic \(Q(x)\) approximation at \(x=0\).

First make a table of derivatives for the functions like this:
\[\begin{cases}f(x) &= \sin(x)\\ f'(x) &= \cos(x)\\ f''(x) &= -\sin(x)\end{cases}\]
Then make a table of derivatives for the LINEAR approximation like this:
\[\begin{cases}L(x) &= Ax + B\\ L'(x) &= A\end{cases}\]
Then make a table of derivatives for the QUADRATIC approximations like this:
\[\begin{cases}Q(x) &= Ax^2 +Bx +C\\Q'(x) &= 2Ax + B\\Q''(x) &= 2A\end{cases}\]
Then EVALUATE the function at the given point \(x=0\)
\[\begin{cases}f(0) &= \sin(0) & = 0\\ f'(0) &= \cos(0) &= 1\\ f''(0) &= -\sin(0) &= 0\end{cases}\]
Then EVALUATE the QUADRATIC approx at the given point \(x=0\)
\[\begin{cases}Q(0) &= A(0)^2+B(0)+C &= C\\ Q'(0) &=2A(0)+B &= B \\ Q''(0) &= 2A &=2A \end{cases}\]
Then EVALUATE the LINEAR approx at the given point \(x=0\).
\[\begin{cases}L(0) &= A(0) + B & = B \\ L'(0) & = B & = B \end{cases}\]
Now we match up the coefficients. Let's do this for the Quadratic approximation first.
\[\begin{cases}f(0) = 0 = Q(0) = C\\ f'(0) = 1 = Q'(0) = B \\ f''(0) = 0 = Q''(0) = 2A\end{cases}\]
Hopefully it is obvious that \(C = 0, B = 1, \text{ and } A = 0\) which means our QUADRATIC approximation to \(f(x) = \sin(x)\) at \(x=0\) is \(Q(x) = x\) (because \(Q(x) = Ax^2 + Bx +C\) )
Do the same thing for the linear approxmation! :)

Answer 12

I think you messed up on the Linear approximation. L(x) should be, L(x) = f(a)+f '(a)(x-a)