Some antidiff qstns-please help

[perfectscore]

[IMG]http://img243.imageshack.us/img243/5940/img2498hi3.th.jpg[/img]

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I'm not so sure how to begin; so just tell me how to start off!
Thanks in advance :]

[dcc]

tell us what you have tried, people are not here to do your SACs for you.

[Mao]

the easiest way to start is to draw the graph

[Collin Li]

How to get started:

Question 1

i) Draw the graph. The height will be the maximum of the graph minus the minimum of the graph. Keep in mind there is a domain, so the minima and maxima could be the endpoints (it turns out at least one is, since there is only one stationary point).

ii) Use volumes of revolution. Set up your integral, and then you can use your calculator to evaluate it (it asks for 2 decimal places).

iii) Use volumes of revolution again, but this time you have to think about your terminals. You have to use calculus this time.

iv) Use the solution to part (ii). Let's call that . Solve for when . You may use your calculator here.

v) Differentiate your expression in part (iii) with respect to .

vi) Use related rates.

To find , use the chain rule with:

and .

You'll also need to substitute a few values in ()

[Collin Li]

Question 2

i) The curve is a parabola:

The base has a radius length of 15, with the y-axis () as the central axis, which means the x-intercepts are: .

Hence:

Also, we know the coordinates at the top of the bowl:
and

Use any of those points on the above equation to find the value of , and then expand the expression to prove it.

ii) Use volumes of revolution on the parabola. You are rotating about the y-axis.

iii) Find an expression for . Remember to include the top and the bottom. It will involve calculus. Try to find an integral that will represent the sum of the tiny strips that make up surface of the solid of revolution.

This shouldn't actually be on the course (part iii.) which leads Mao to believe that the they are referring to is just the top (or bottom) surface area. Pretty ambiguous question. You will need clarification, or you can just work it out (since you know what you're aiming for -- it gives you the answer)

Summary: This whole SAC (or whatever it is) is easy, except Question 2 part iii.

[Mao]

iii) Find an expression for . Remember to include the top and the bottom. It will involve calculus. Try to find an integral that will represent the sum of the tiny "rectangular strips" that make up surface of the solid of revolution (remember the theory of solids of revolution is based on cylinders).

This shouldn't actually be on the course (part iii.) which leads Mao to believe that the they are referring to is just the top (or bottom) surface area. Pretty ambiguous question. You will need clarification.

Summary: This whole SAC (or whatever it is) is easy, except Question 2 part iii.

I have checked part iii, my assumption is correct. It does refer to the area of the water, i.e. the top area where water is exposed to air.

terribly worded question.

[perfectscore]

sorry; i could do all of qstn 2; i forgot to put the qstns i couldn't do - the page was double sided!!

continued from q2
(iv) find the relationship between V and h {use part (ii) and make the terminals be 'h'?}
(V) consturct a differential. eqn expressing dh-dt as a function of h {chain rule?}
(vi) find the time taken for the container to empty {i keep on getting 'dodgy' numbers?!}

[ganges]

ANother question.........

Antidifferentiate

SIN(inverse)(X/2)? Without a calc....


I thought u cant anti diff inverse?

[ed_saifa]

ANother question.........

Antidifferentiate

SIN(inverse)(X/2)? Without a calc....


I thought u cant anti diff inverse?

Thats beyond the scope of the specialist course unless more information is given such as integration by recognition.

[ganges]

yeh i got it from itute........

[ed_saifa]

Itute exams are way above the required level.

[ganges]

Heres another one, anti differentiate

x sinx.

[phagist_]

Pretty sure that's not in spesh course either (Integration by parts)

[/0]

Heres another one, anti differentiate

x sinx.

Hint: differentiate

[Mao]

ANother question.........

Antidifferentiate

SIN(inverse)(X/2)? Without a calc....


I thought u cant anti diff inverse?

try differentiating