4U Maths Question Thread

[RuiAce]

at y=f^2 (x)

why is the turning point squared of f(x)?? i dont get it :/

For the sake of disambiguity, are you referring to \(f(f(x))\) or \([f(x)]^2\)?

[itssona]

For the sake of disambiguity, are you referring to \(f(f(x))\) or \([f(x)]^2\)?

f(f(x))

[RuiAce]

In general, no rule immediately justifies how to find the values of x satisfying that criteria. These zeroes can potentially be hard to find

[itssona]

In general, no rule immediately justifies how to find the values of x satisfying that criteria. These zeroes can potentially be hard to find

oh that makes sense!

sorry to ask another thing, but does that mean:
if I graph y=(x^2 -1)^3 then I can see that f'(x) is 0 so we have x = + or -1
and then I make this function in terms of f(x) and see that x=0

[RuiAce]

[RuiAce]

oh that makes sense!

sorry to ask another thing, but does that mean:
if I graph y=(x^2 -1)^3 then I can see that f'(x) is 0 so we have x = + or -1
and then I make this function in terms of f(x) and see that x=0

Not too sure what you mean here?

[itssona]

Not too sure what you mean here?

like you know how f(x) should =0 because f cube x 's derivative is f'(x) multiplied by derivate of f'f(x) (and this is made up of f(x) and f'(x))

so what I mean to say is that f(x) should be 0

soooo (x^2-1)^3 =0
and then x=0

Im probably wrong lol idk

[RuiAce]

[itssona]

ah I get you

ohh I get you! Thank you SOO much for explaining all this so well Rui

[seventeenboi]

Hi! pls help with the 'describe how the shape of this curve changes as λ increases from 1 towards 2' part
Thanks!

[RuiAce]

Hi! pls help with the 'describe how the shape of this curve changes as λ increases from 1 towards 2' part
Thanks!

GeoGebra simulation attached

[scienceislife]

Evaluate the integral between 0 and -1 sqrtx+2/sqrt1-x dx
Thank you!

[RuiAce]

Evaluate the integral between 0 and -1 sqrtx+2/sqrt1-x dx
Thank you!

For the sake of disambiguity, do you mean \( \frac{\sqrt{x+2}}{\sqrt{1-x}}\), \(\frac{\sqrt{x}+2}{\sqrt{1}-x} \) or \(\sqrt{x}+\frac{2}{\sqrt{1}}-x \)?

The way you have typed it (without bracketing) is implied to suggest that you mean the third one.

[bluecookie]

What's the focus and directrix of a line? (with e=infinity)

[RuiAce]

What's the focus and directrix of a line? (with e=infinity)

In essence, we will have a pair of intersecting lines and not just a single line.

Consider what happens as the eccentricity is increased. As the eccentricity increases, the foci become further distanced and the directrices approaches the y-axis. When the eccentricity becomes infinite, the foci will be infinitely away and the directrices coincide on the y-axis.

This also makes intuitive sense, as PS/PM = e. As e->inf, we have either PS -> inf, or PM -> 0.

It may be worth considering that this case is the opposite of the circle, where the foci coincide at the origin to become the centre, and the directrices are infinitely far away