revision on integration and differentiation

- AravindG

revision on integration and differentiation

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- schrodinger

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- AravindG

hey!

- AravindG

shall we start

- AccessDenied

certainly

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## More answers

- anonymous

follow this http://www.bbc.co.uk/scotland/learning/bitesize/higher/maths/calculus/

- AravindG

1.Find the maximum value of the product of 2 nos if their sum is 12

- AccessDenied

So, we're maximizing "xy" if "x + y = 12"...
I think if we rewrite the second equation with an independent variable, then we can clean up the first expression as a one-variable expression, and then find the horizontal tangent of that
x + y = 12
y = 12 - x
xy <- y=12-x
x(12 - x)

- AravindG

hmm then?

- AccessDenied

you can multiply it out and then take the derivative
once you have the derivative, you set that equal to 0 to find the point of a horizontal tangent, since that will be the maximum (not really rigorous in showing that, but its an upside-down parabola so it has one horizontal tangent at the maximum point)

- AccessDenied

x(12 - x) = 12x - x^2
d/dx( 12x - x^2 ) = 12 - 2x
12 - 2x = 0
-2x = -12
x = 6
then we have to go back to that equation to find y's value
y = 12 - x
y = 12 - 6
y = 6
xy = 6(6)
= 36

- AravindG

wow thanks next one

- AravindG

2 A printed page is required to contain k square units of printed matter .Side margins of width a and top bottom margins of width b are required .Find the length of the printed lines when the page is designed top use the least paper

- AccessDenied

is that all the information?

- AravindG

ys

- AccessDenied

interesting... i'll have to think about that one a bit

- AravindG

k post it here when u get an idea iw ill wait

- AccessDenied

|dw:1333259293620:dw|
Well, since there's no numerical information given, i think the final answer isn't going to be a number, probably an expression with the k.
That's the picture... hmm

- AravindG

hmmm

- AccessDenied

Well, I'll start with
x := length of a printed line
y := amount of printed matter (vertically)
|dw:1333259779521:dw|
"xy = k" is the equation for square units of printed matter on the page.
The dimensions of the page itself are "2a + x" by "2b + y"

- AravindG

k

- AravindG

then?

- AccessDenied

I'm not quite sure what the question is asking... anybody else know? :P

- AravindG

anyone>>

- AravindG

hmm

- AravindG

well u think abt it lets go to thenext one then

- AravindG

3.Prove that the fn f(x)=2sinx +tanx -3x is increasing in the interval (-90,90)

- anonymous

Is the paper a square?

- AravindG

dunno i hav only the info in the qn

- AravindG

acces any idea abt the 3rd qn?

- AccessDenied

i graphed it, it doesnt really look like that function is even increasing in that interval...

- AravindG

oh thn how?

- AravindG

pls try again i am sure the qn is crct

- AccessDenied

odd, the derivative is always positive on the interval (so the function should be increasing), but the actual function itself looks like its decreasing on the graph? o.O

- AravindG

oh !

- AravindG

wel u think ovr abt that one too next qn

- AravindG

Find the intervals of monotonicity of the function y=2x^2-log|x|,x!=0 .Hence find the points of maximum and minimum

- AravindG

access?

- AccessDenied

you'd find the derivative and set it equal to 0... except im not sure on the absolute value there.
2x^2 - log|x|
derivative of 2x^2 is 4x, the derivative of log(x) is 1/(x*ln(10))... but that absolute value gets me

- AravindG

y?? it is said in qn dont consider case of 0

- AccessDenied

oh, not only =0, also points where graph is undefined*
the question only says x=/= 0

- AravindG

wat

- AccessDenied

if i knew the derivative of log|x|, i could possibly give you a better explanation using an example
but points where the derivative is undefined are also critical points when the function exists at that point

- AravindG

derivative of log mod x is 1/x

- AccessDenied

uhh, sorry, not sure i can help you with these questions. they're a bit outside of what i know. :)

- AravindG

last one

- AravindG

20 m of wire is available to fence off a flower bed in the form of a circular sector.what must be the radius of the circle oif we wish to have a flower bed with greatest possible area?

- anonymous

May I help?

- AravindG

ys

- AccessDenied

You may help. :)
I have an idea of how to do that last one, unless that's what you know. :P

- AravindG

both of u bring in ur best n fast :P

- anonymous

As there are 20 m fence, 2r pi =20, r=10
A=r^2 pi
A'=2 pi r
A''= 2pi >0
therefore, max A occurs at r=10
A=(10)(10) pi =314

- AccessDenied

its not a full circle, but a sector of a circle

- AravindG

wt u think access?

- AravindG

tell ur method

- AccessDenied

So, the perimeter of the sector is: P = 2r + rt (t := angle between radii that make up the sector).
P is also given to be 20.
20 = 2r + rt
The area of the sector is A = r^2 t/2.
If we use substitution to get a function of t with respect to r...
20 = 2r + rt
20 = r(2 + t) r=/=0
20/r = 2 + t
20/r - 2 = t
A = r^2 (20/r - 2) / 2
= ( 20r^2 / r - 2r^2 ) / 2
= 10r - r^2
A' = 10 - 2r
10 - 2r = 0
-2r = -10
r = 5

- AravindG

yey thx a lot

- AravindG

do post here if u get better attempts on the qns we skipped

- AccessDenied

i actually found the solution online for the one concerning the page and print matter
the answer just isnt intuitive for me, trying to think of a way to explain it. they basically used a function of area of the page to the x-value (substitution from k=xy) and minimized the area of the page

- AravindG

help

- anonymous

Any other question?

- AravindG

HMM?u knw integration and differentiation?

- anonymous

No, but the type of questions u posted, I think I can solve by any other method also.

- AravindG

did u get the book qn?

- anonymous

Which one? The "Page" Question????????

- AravindG

ys

- anonymous

See bhai, @AccessDenied answer is right. But after that, how to proceed not exactly getting. What to find next????????????? Any more options and clues given?????????

- AravindG

nop

- anonymous

In that case, @AccessDenied answer is rite.

- AravindG

can u help with that page qn?

- anonymous

ok. lemme try first. i didn't read the whole post was it resolved?

- AravindG

no

- anonymous

|dw:1333355356996:dw|

- AravindG

cntinue

- AravindG

wt to do next?

- anonymous

|dw:1333355572827:dw|