VCE Methods Question Thread!

[colline]

Why is the inverse function of f(x)= e^2x for x ∈ R⁺ equal to

If you swap the x and y for the inverse, you would get


Then take log of both sides




Log_e(e) cancels out




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Hi,

I am having trouble with part d) of this question. It follows on with other parts of a question which I have attached. I have written that 'p' can indeed have stationary points but am not sure what the possible values of 'p' could be. If anyone can list these possible values that would be great, as this is apart of a big assignment that is due soon. Please note this is from question 4 from the first picture.

Thank You and Kind Regards.

I think it's just a complicated way of wording "how many stationary points can the graph of a quartic function have". A quartic function must have at least 1 stationary point and at most 3, so P = 1, 2, or 3.

[^^^111^^^]

(Sorry for the double post, but this is a different question).

Could you elaborate by perhaps providing an example of a question?

The specific concept of osculating circles isn't mentioned in the study design, but it wouldn't be too hard for VCAA to integrate it into a question.

The current VCE Mathematics study design can be found here.

Thank you

[xXMJ7Xx]

Hi,
I have a question about Methods Unit 4, in Integration (calculus) topic/SAC, do we have to know things about the absolute value function.

[galaxy21]

Hey,
I have been doing some application questions for calculus of logs, and I keep getting stuck on the same part.

For questions like this one, I can do part a and b fine, but for part c I just get lost on how it all connects. Is someone able to explain how to work it out? How is the inverse function involved??
Thanks!

[Tau]

Hi,
I have a question about Methods Unit 4, in Integration (calculus) topic/SAC, do we have to know things about the absolute value function.

Absolute value functions aren’t part of the Methods Study Design any more. They are a part of Specialist though. I believe the only place absolute value functions are mentioned in Methods is in the textbook when discussing differentiability at a point.

[Tau]

Hey,
I have been doing some application questions for calculus of logs, and I keep getting stuck on the same part.

For questions like this one, I can do part a and b fine, but for part c I just get lost on how it all connects. Is someone able to explain how to work it out? How is the inverse function involved??
Thanks!

a) Solve for x-int, where
b)
c) This is an integration by recognition problem. We need to use the answer in part b to find the integral of to find the area of the shaded region.

.

Now, to calculate the area we are looking for the integral from 1/2 to 2:
square units.

[TyranT]

Hello, If someone could help me just grasp how to do solve; it would be great. I know how to rationalise it into two different fractions but not into one.
Help would be very much appreciated.
Thanks

[Remy33]

Hello, If someone could help me just grasp how to do solve; it would be great. I know how to rationalise it into two different fractions but not into one.
Help would be very much appreciated.
Thanks

Think you gotta add the two together first by making sure both have the same denominator, once you've turned it into one fraction you can rationalise it.

[TyranT]

Could you please do the first as an example. I end up with the square root of 2

[Remy33]

Could you please do the first as an example. I end up with the square root of 2

How did you get that?

I did:

[^^^111^^^]

Could you please do the first as an example. I end up with the square root of 2

First rationalise 3 / root 2. (U  basically times the  top and bottom by root 2). U will now end up with 3* root 2 / 2.

Next find a common denominator to solve the fraction. This will then become 2/6  + 9*root 2 /6. Add these two to get 2 + 9(root 2 ) whole divided by 6. Then once again rationalize. Does that help?

[^^^111^^^]

I will probably just do question 2 as well, in case u r still confused. Multiply the numerator and denominator of 1/root 3  by root 3. Do the same for 4 by root 5 (except root 5 for this). Now find the common denominator (15). The fractions will then become 12 root 5 for the numerator of the first fraction and 5 root 3 for the numerator of the second fraction. Thus the final answer is (12 root 5 - 5 root 3)/ 15. Hope that helps. (I'm really sorry I'm new and don't know how to use latex yet   .

[pugs]

hii, would anyone be able to help me explain how the 5 gets pulled out from the f(x/5)? there's an answer in the back of the checkpoints but i don't really understand it :/

if 5 is pulled out, wouldn't the x/5 inside of f() need to be 5x? (sorry if it's a dumb Q!)

& thank you very much in advance!

[Matthew_Whelan]

hii, would anyone be able to help me explain how the 5 gets pulled out from the f(x/5)? there's an answer in the back of the checkpoints but i don't really understand it :/

if 5 is pulled out, wouldn't the x/5 inside of f() need to be 5x? (sorry if it's a dumb Q!)

& thank you very much in advance!

As the integral of f(x) = a, the integral of f(x/5) would be 5a I think.
This would mean the answer would be 2(5a + 15a) = 40a.

[TyranT]

Hello, I have a question:
It says 'write the following expression as a single power: 7 root 7' To clarify that means 7 multiplied by the root of 7.

Any help would be much appreciated.
Thanks