VCE Methods Question Thread!

[Stick]

Alright, let's break down the expression on the left, step by step.





(applying the relevant logarithm law)

(simplifying)

( and cancel each other out)

If you still don't quite understand, please don't hesitate to ask for help. I hope you get it now.

[soNasty]

Alright, let's break down the expression on the left, step by step.





(applying the relevant logarithm law)

(simplifying)

( and cancel each other out)

If you still don't quite understand, please don't hesitate to ask for help. I hope you get it now.

thankyou!

[Snorlax]

In composite functions we never expand right?
eg,





Leave it as it is? Or expand?

Cheers,

[Phy124]

In composite functions we never expand right?
eg,





Leave it as it is? Or expand?

Cheers,

I'm relatively certain that it doesn't matter. However, I would think it's much handier to have it in the form you have as straight away you know where the x-intercept and  turning point are and you can also find the y-intercept almost effortlessly.

[soNasty]

given that

how do i show that this is false? (false is the answer)

[psyxwar]

given that

how do i show that this is false? (false is the answer)

f(x)=ln(x^2)
f(y) =ln(y^2)
f(x)+f(y)=ln(xy)^2

f(x^2y^2) = ln(xy)^4

ln(xy)^4 =/= ln (xy)^2

[soNasty]

f(x)=ln(x^2)
f(y) =ln(y^2)
f(x)+f(y)=ln(xy)^2

f(x^2y^2) = ln(xy)^4

ln(xy)^4 =/= ln (xy)^2

thanks! just wondering, if .. WHY cant it be

[psyxwar]

thanks! just wondering, if .. WHY cant it be

I'm not too sure what you're asking here, but f(x)+f(y) is the same as f(xy) due to the nature of the log laws

[soNasty]

I'm not too sure what you're asking here, but f(x)+f(y) is the same as f(xy) due to the nature of the log laws

oh wow sorry i get it now, i misread it! thanks again

[soNasty]

another q

if f(x) = e^(7x-2)
given find the value of b

how would i do that?

[b^3]

If you have , then you replace with in your expression for . (As is an expression that you're putting into the function to output another expression or value depending on what function you're putting it through).
e.g.

So what we can do is equate the relevant expressions and then collect together like terms, then equate coefficients to find .

[soNasty]

If you have , then you replace with in your expression for . (As is an expression that you're putting into the function to output another expression or value depending on what function you're putting it through).
e.g.

So what we can do is equate the relevant expressions and then collect together like terms, then equate coefficients to find .

thankyou

[psyxwar]

If had to find the rate of change of volume with respect to height given that and that at the point where h=2, why does it make a difference if I substitute first and differentiate the expression and then substitute h=2 in, rather than substituting r for (the value of r when h is 2) and differentiating that?

[Yacoubb]

x+3
___

2x - 1

Could someone show me how to get that into the form a/ ( x+ b) + c

[psyxwar]

x+3
___

2x - 1

Could someone show me how to get that into the form a/ ( x+ b) + c

ok you can long divide but if you're just trying to sketch it that's not necessary.



If we allow x to approach infinity, the two fractions approach 0 and become negligible. Hence, there is an asymptote at , or y=(coefficient of x in numerator)/(coefficient of x in denominator)

The other asymptote is when the function is undefined, or when the denominator equals zero. Hence, there is another asymptote at x=1/2

From this info you can just work out the intercepts and sketch the graph.