VCE Specialist 3/4 Question Thread!

[Limista]

Euler's formula Exercise 9G in the Essentials textbook: do we need to know how to do all that programming with our calculator?

Also, all the questions in this chapter require the calculator (am I right??) , and I don't know how to do all that programming on my calculator

[Homer]

sketch [0.5,8]->R, f(x)=

Let the points on the curve which represent the domain endpoints be A and B. The maximum angle of deviation is the angle AOB, where O is the origin. Find the maximum angle of deviation to the nearest degree.
 

[SocialRhubarb]

Use .

Spoiler

Our two endpoints are and

Find the equations of the lines which pass through these end points and the origin.

   and    Let be the angle between and the x-axis, and be the angle between and the x-axis.





Alternatively, you can use the tan trig identities:





Or even recognising that the graph is symmetrical about the line y=x, so that

[Homer]

okay well I drew a triangle OAB

the side length from A to B worked out to be

the side length from O to A and O to B was the same ->

then when i try to find the angle

i get 86 degrees instead of 83(82.8 ) as worked in the post above.

where am i going wrong?

[SocialRhubarb]

Cosine rule:

[Solidarity]

I'm just wondering how I should go about trying to integrate this function


any help would be appreciated!

MOD EDIT: Merged threads and removed duplicate post

[abeybaby]

is the denominator e^(3x+1) or e^(3x)+1?

[lzxnl]

I am going to assume you mean




I trust you can do the rest.

[b^3]

Note: Please don't post the same question in multiple threads. Merged the old thread with the Specialist Question Thread.

[barydos]

Hi, this is probably pretty simple but
I just have a question regarding differential equations.
How am I able to assume the condition in the following image:

Spoiler

after integrating?

[b^3]

When you integrate you get . The only result that will be able to satisfy the initial condition will be , as the other result will give a negative inside the log (e.g. , ). Now this is also where the restriction comes in, what we have inside the log has to be greater than zero (as that is our domain for a simple log function, it won't accept 0 or negative values). So which means we have

[barydos]

When you integrate you get . The only result that will be able to satisfy the initial condition will be , as the other result will give a negative inside the log (e.g. , ). Now this is also where the restriction comes in, what we have inside the log has to be greater than zero (as that is our domain for a simple log function, it won't accept 0 or negative values). So which means we have

Wow, I totally derped out there. Thanks a lot, b^3!

[Nato]

complex numbers here

so i have to find the polar form of

i have put my working in spoilers. the answer i got but the answers say 

Spoiler

so i found the modulus as so from the triangle on the argand plane i found which is . then for which also equals

so i recognised that this was in the third quadrant so did so this resulted in my answer of
.

can anybody help me with where i went wrong

[lzxnl]

The two answers are exactly the same numerically, it's just that your answer is non-Standard. It's convention to have the argument in the range , and your argument of is unfortunately outside this range. Subtracting from your argument gives the solution provided.

[Jaswinder]

could someone help me with    f, g and h?  thanksssss

sorry: forgot to upload