User:Arctanx.tk

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[edit] Maximum Power Transfer

in the notes, he says P = \textrm{Re}\left\{ \frac{V_s^2 \left( R_L + jX_L\right) }{ (R_S+R_L)^2 + (X_S+X_L)^2} \right\} but in the derivation the denominator is \left[(R_S+R_L) + j(X_S+X_L)\right]^2 which doesn't expand out. I'm wondering if you could have a look at your notes to see if they match

[edit] Question 5a

Evaulate \int_0^2 (x^2+1)dx by calculating \lim_{||P||\rightarrow 0} \sum_{i=1}^{n} f(x_i^*)\Delta x_i, where P is the partition of [0,2] into n equal intervals and x_i^* is the right end of the ith. subinterval.

(Hint: \sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6})

[edit] The Sum Thing

\sum_{x=1}^{n} f(x) means that you take f(1), f(2), f(3), etc. up to f(n), and add them all together.

For example,

\sum_{x=1}^{5} 2x = 2(1) + 2(2) + 2(3) + 2(4) + 2(5) = 30

Note that:

\sum_{x=1}^{5} 2x = 2\sum_{x=1}^5 x

and that a rule exists that

\sum_{x=1}^{n}x = \frac{n(n+1)}{2}

so

\sum_{x=1}^{5} 2x = 2\sum_{x=1}^5 x = 2 \frac{5(5+1)}{2} = 2 \frac{30}{2} = 30