User:Arctanx.tk

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

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 $$i$$th. subinterval.

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

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

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