VCE Methods Question Thread!

[Homer]

how would i differentiate f(x)=sin(x)^cos(x)

[pi]

Hint: Try the chain rule

[dinosaur93]

for probability

what is the difference between discrete random distributions, binomial distributions, normal standard distribution and continuous random variables?

[TrueTears]

A binomial discrete distribution is a discrete distribution.

But not all discrete distributions are binomial.

Similarly, a normal random variable is a continuous random variable but not all CRV's are NRV's

[Jenny_2108]

for probability

what is the difference between discrete random distributions, binomial distributions, normal standard distribution and continuous random variables?

Discrete random distribution: a variable that has a countable number of possible values

Binomial distribution (special case of discrete random distribution): + only 2 outcomes/events: success and failure
                                                                                                    + independent trials, success outcomes are identical
                                                                                                    + Pr(success) = constant

Continous random variables (opposite discrete random distribution): can't calculate Pr of individual values => calculate Pr over a range of values

Normal standard distribution (special case of continuous variables, has bell curve shape):
+ mean: central peak
+ symmetrical about mean
+ standard deviation: determines the spread
+ domain: R

Edit: Beaten by True Tears

[generalkorn12]

If a volume of a cuboid is V=6x^3, find the approximate change in volume from 3 to 3.02, and determine whether this approximation is greater/less than the exact change.

I'm able to do the first part and determine the approximate change (3.02) but don't really understand whether or not it's greater than the exact change. I'm assuming it's greater than, as a chord for a cubic graph at x=3 will always be 'greater' than the tangent at that point... but my teacher says that assumptions wrong. (keep in mind, this teacher doesn't even know the theory behind linear approximation!)

[Hancock]

Well, if you find the approximate change in V, using linear approximation, you'll get

f(x) = 6x^3 = V

f(x+h) = f(x) + hf'(x)            x = 3, h = 2/100, f'(x) = 18x^2

f(3.02) = 6(3^3) + (2/100)(18*3^2)
f(3.02) = 6(27) + (2/100)(162)
f(3.02) = 162 + 3.24
f(3.02) = 165.24

So, the change in V from 3 to 3.02 is 165.24 - 162 = 3.24

If you wanted to know the actual change, you have to draw a cubic graph. Now, you realise that an x^3 graph is always increasing, and that it's derivative is always getting greater with a greater x.

So, f'(3.02) > f'(3)

Since we approximated using the derivative at 3, not 3.02 (which is the point of linear approximation anyway), the change in V will be lower than the actual change.

You can always check it by doing:

V(3.02) - V(3) = 165.2616 - 162 = 3.2616
           

[joseph95]

If you wanted to know the actual change, you have to draw a cubic graph.

That would probably be really unnecessary.
Just performing your last step, V(3.2) - V(3), would be sufficient to determine the exact change.

[Hancock]

Yeah, but it's good to either imagine what's going on or visually see it.

[spaniish.beauty]

which lecture are you guys going to for methods?

are the connecteducation lectures better than engage lectures for the subjects: methods, englih language and biology or?

please give me your opinion, and also as to why

Will be much appreciated ! xx

[HERculina]

How do you solve n(C)5 x (0.6^5) x (0.4)^(n-5) > 0.25 on TI-nspire CAS?

[pi]

nSolve(...) should be able to do it

[HERculina]

So am I suppose to type:
nSolve(nCr(x,5).(0.6^5).(0.4)^(x-5)>0.25,x)?

[FlorianK]

which lecture are you guys going to for methods?

are the connecteducation lectures better than engage lectures for the subjects: methods, englih language and biology or?

please give me your opinion, and also as to why

Will be much appreciated ! xx

defs better for methods, no idea about the rest

[Jenny_2108]

^ Bio is good as well. Eddie is great