open book test (1 Viewer)

[xotic_rose]

okay... so we have an open book test coming up... so naturally the questions are gonna be shit hard. we had our 2u one last week, and i swear to goodness it was harder than any test i have ever done in my life!! this 3u test, is SUPPOSED to be hard (whereas our teachers stupidly thought the 2u test was easy). Sooo... I have this one request...
can u people PLEASE PLEASE PLEASE post up really hard 3u questions... if possible with an explanation, so i might have see what i have to fair against on wednesday. PLEASE!! I am not a threat to anyone's university placing... lol... I am content with staying in wollongong...
Thankyou sooo much...
Maryyyyyyyyyyyy

 

[Eagles]

Whats your test on? i.e. what topic(s)

 

[xotic_rose]

intergration (volume and area)
newtons and approximation methods
inverse trig
rates of change

 

[Xayma]

Open Book Test, can you bring in sheets of paper? If so put all your formulas on it and some examples if you need to, that way you wont spend ages flicking through the book to find them.

 

[George W. Bush]

Find the area under the curve e^(x^2) from 0 to e.

 

[Harimau]

(From James Ruse's 1997 paper)
Find the exact volume generated when the region bounded by the functions y = e^x and x = ln2 and the co-ordinate axes is rotated about the x-axis.

(This one i made up... Hee Hee Hee, its not too hard, its just long. I know its not exactly a pyramid, but i can't remember the real name for it... You'd have to derive a formula for the volume of such a shape first, it would require a lot of thinking. This should be a piece of cake for 4 unit students)

The surface area of a pyramid with an octagonal base is expanding at a rate of 5 cm/sec. Find the rate at which the volume is increasing relative to (i) its Hadius (ii) Its Surface Area (iii) Its Perpendicular Height if it is given that the semi vertical angle of the pyramid is A degrees. 0 < A < 90

 

[Affinity]

Originally posted by George W. Bush
Find the area under the curve e^(x^2) from 0 to e.

corrected to 2 decimal places.

2.) Express the volume of the solid formed by rotating the region bounded by x = 1, y = 1/x, y = e^(-x) and x = k (k>1) as a definite integral.
Suppose k increases at a rate of a units per second, find the rate of change of the volume of the solid.


3.) Romeo and Juliet affection for each other could be guaged by the quantities R and J respectively. Being a simple guy, Romeo's affection for juliet grows at a rate proportional to juliet's affection for him, the constant of proportionality being A. Juliet, however is more complicated, the more Romeo loves her, the faster she becomes annoyed with Romeo's advances. this relation is also linear, with constant of proportionality being B.

if R is initially at 1, express R as a function of t.