- gods are discriminatory/corrupt/voltaile
- gods' ignorance is detrimental to Trojans
- Athene - submits to Poseidon
+
+> In Euripides' *The Women of Troy*, the women are all passive victims
+
+Victims of hardship are typically cautious to fight back and hence are passive to further suffering. However, Euripides emphasises how this is not necessarily true, and exemplifies this through the responses of some of the women. There is a great contrast in the responseses to the d...
+
+### Paragraphs
+
+1. Women have no choice, they are passive by force
+2. They appear passive to outsiders but their rebellion within each other motivates them
+2. Hecuba is not passive
+3. Cassandra is not passive
+
+Hardship and opression inevitably forces individuals into a corner of helplessness and lament, and this is a prominent theme in Euripides' *Women of Troy*. However, despite the grief and loss that the women experience, they express a subtle element of rebellion and rejection of their inhumane treatment. As the women are gruesomely tortured by the Greeks, they have little room to object to their abuse, but Euripides emphasises how they do everything in their power to rebel against it. As a result, the play shows how those who are opressed by inhumane treatment are not necessarily forced into passivism, and that rebellion and activism always has some benefit to the individuals.
+
+The characters in *Women of Troy* are
+
+> Euripides' *Women of Troy* is not only an innovative perspective on the aftermath of the Trojan War, but also a portrayal of the barbaric actions of the Greeks towards the women and children the subjugated in the defeat of Troy. Discuss.
+
+1. Aftermath of war
+2. Barbaric actions of greeks
+
+Women
+- what happened to them
+- imagery (violent, vivid) - depicts the women as lamenting. Loss of life, uncertain future, devestation
+
+Innovative perspective
+- strength of the women of Troy
+- condemning of Greeks
+- Condemning war
+- actions have consequences.
+- focus on the victims
+- direct reaction to Melos
+- women aren't always passive victims
+
+Greeks
+- journey back to Athens
+- Gods impact on the trip
+- loss of life
+- loss of courage
+- loss of humanity
- war effects everyone (e.g. Astyanax) therefore everyone should see the brutal outcome
- acknowledgement that children should not be involved
+
+## Extra English 3/4/19 - Building complexity
+
+### Structure
+
+- interesting opening statement/quote
+- background hooks
+- link topic to views & values
+- do not list points
+- emotional engagement - e.g. poignantly, "barbaric cruelty" etc
+- do not evaluate play
+
+### Vocabulary
+
+- make a list of useful words/synonyms for essays
+- suffering/grief, comfort, cruelty, condemnation, hope
+
+### Ideas
+
+- subtlties of characters - offer rebuttals/contrasts
+- subtle differences between characters
+
+### Detailed knowledge
+
+- discuss >1 character / paragraph
+- focus on ideas/motifs in paragraphs, not characters
+- comment on stage directions, context etc
+
+### Views and values
+
+- rewrite link sentences as views & values statements
+- develop a personal interpretation of the text
+- consider how Taylor's translation impacts the message
+- context (time, society etc) - Euripides warns his contemporaries against war
+- women - Hecuba's power over men vs Helen's power over women
+
+### Text construction
+
+- motifs/images - water, song/dance, animals (dehumanisation), personification of Troy
+- graphic depictions of violence & dehumanisation
+- entire play is like its own ending/conclusion (lamenting, despair)
+- gods do not care about Trojans, but readers do
+- discuss significance of single characters and representation of groups, e.g. Talthybius & Menelaus are the only Greek characters.
+
--- /dev/null
+# Inverse functions
+
+## Functions
+
+- vertical line test
+- each $x$ value produces only one $y$ value
+
+## One to one functions
+
+- $f(x)$ is *one to one* if $f(a) \ne f(b)$ if $a, b \in \operatorname{dom}(f)$ and $a \ne b$
+- i.e. unique $y$ for each $x$ ($\sin x$ is not 1:1, $x^3$ is)
+- horizontal line test
+- if not one to one, it is many to one
+
+## Inverse functions $f^{-1}$
+
+- if $f(g(x)) = x$, then $g$ is the inverse of $f$
+- reflection across $y-x$
+- $\operatorname{ran} \> f = \operatorname{dom} \> f^{-1}, \quad \operatorname{dom} \> f = \operatorname{ran} \> f^{-1}$
+- inverse $\ne$ inverse *function* (i.e. inverse must pass vertical line test)
+- - $\implies f^{-1}(x)$ exists $\iff f(x)$ is one to one
+- $f^{-1}(x)=f(x)$ intersections may lie on line $y=x$
+
+Requirements for showing working for $f^{-1}$:
+
+- start with *"let $y=f(x)$"*
+- must state *"take inverse"* for line where $y$ and $x$ are swapped
+- do all working in terms of $y=\dots$
+- for square root, state $\pm$ solutions then show restricted
+- for inverse *function*, state in function notation
+## Implicit Differentiation
+
+On CAS: Action $\rightarrow$ Calculation $\rightarrow$ `impDiff(y^2+ax=5, x, y)`. Returns $y^\prime= \dots$.
+
+Used for differentiating circles etc.
+
+If $p$ and $q$ are expressions in $x$ and $y$ such that $p=q$, for all $x$ nd $y$, then:
+
+$${dp \over dx} = {dq \over dx} \quad \text{and} \quad {dp \over dy} = {dq \over dy}$$
+
## Antidifferentiation
$$y={x^{n+1} \over n+1} + c$$
## Integration
-$$\int f(x) dx = F(x) + c$$
+$$\int f(x) dx = F(x) + c \quad \text{where } F^\prime(x) = f(x)$$
- area enclosed by curves
- $+c$ should be shown on each step without $\int$
| $g^\prime(x)\cdot f^\prime(g(x)$ | $f(g(x))$ (chain rule)|
| $f(x) \cdot g(x)$ | $\int [f^\prime(x) \cdot g(x)] dx + \int [g^\prime(x) f(x)] dx$ |
+### Definite integrals
+
+$$\int_a^b f(x) \cdot dx = [F(x)]_a^b=F(b)-F(a)_{}$$
+
## Applications of antidifferentiation
- $x$-intercepts of $y=f(x)$ identify $x$-coordinates of stationary points on $y=F(x)$
$${d^2 \over dx^2} = {d(y^\prime) \over dx} = {{dy^\prime \over dt} \over {dx \over dt}} \> \vert \> y^\prime = {dy \over dx}$$
-# Rational functions
+## Rational functions
$$f(x) = {P(x) \over Q(x)} \quad \text{where } P, Q \text{ are polynomial functions}$$
-## Addition of ordinates
+### Addition of ordinates
- when two graphs have the same ordinate, $y$-coordinate is double the ordinate
- when two graphs have opposite ordinates, $y$-coordinate is 0 i.e. ($x$-intercept)
- when one of the ordinates is 0, the resulting ordinate is equal to the other ordinate
-