AravindG
  • AravindG
revision on integration and differentiation
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
AravindG
  • AravindG
hey!
AravindG
  • AravindG
shall we start
AccessDenied
  • AccessDenied
certainly

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anonymous
  • anonymous
follow this http://www.bbc.co.uk/scotland/learning/bitesize/higher/maths/calculus/
AravindG
  • AravindG
1.Find the maximum value of the product of 2 nos if their sum is 12
AccessDenied
  • 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
  • AravindG
hmm then?
AccessDenied
  • 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
  • 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
  • AravindG
wow thanks next one
AravindG
  • 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
  • AccessDenied
is that all the information?
AravindG
  • AravindG
ys
AccessDenied
  • AccessDenied
interesting... i'll have to think about that one a bit
AravindG
  • AravindG
k post it here when u get an idea iw ill wait
AccessDenied
  • 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
  • AravindG
hmmm
AccessDenied
  • 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
  • AravindG
k
AravindG
  • AravindG
then?
AccessDenied
  • AccessDenied
I'm not quite sure what the question is asking... anybody else know? :P
AravindG
  • AravindG
anyone>>
AravindG
  • AravindG
hmm
AravindG
  • AravindG
well u think abt it lets go to thenext one then
AravindG
  • AravindG
3.Prove that the fn f(x)=2sinx +tanx -3x is increasing in the interval (-90,90)
anonymous
  • anonymous
Is the paper a square?
AravindG
  • AravindG
dunno i hav only the info in the qn
AravindG
  • AravindG
acces any idea abt the 3rd qn?
AccessDenied
  • AccessDenied
i graphed it, it doesnt really look like that function is even increasing in that interval...
AravindG
  • AravindG
oh thn how?
AravindG
  • AravindG
pls try again i am sure the qn is crct
AccessDenied
  • 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
  • AravindG
oh !
AravindG
  • AravindG
wel u think ovr abt that one too next qn
AravindG
  • 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
  • AravindG
access?
AccessDenied
  • 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
  • AravindG
y?? it is said in qn dont consider case of 0
AccessDenied
  • AccessDenied
oh, not only =0, also points where graph is undefined* the question only says x=/= 0
AravindG
  • AravindG
wat
AccessDenied
  • 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
  • AravindG
derivative of log mod x is 1/x
AccessDenied
  • AccessDenied
uhh, sorry, not sure i can help you with these questions. they're a bit outside of what i know. :)
AravindG
  • AravindG
last one
AravindG
  • 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
  • anonymous
May I help?
AravindG
  • AravindG
ys
AccessDenied
  • AccessDenied
You may help. :) I have an idea of how to do that last one, unless that's what you know. :P
AravindG
  • AravindG
both of u bring in ur best n fast :P
anonymous
  • 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
  • AccessDenied
its not a full circle, but a sector of a circle
AravindG
  • AravindG
wt u think access?
AravindG
  • AravindG
tell ur method
AccessDenied
  • 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
  • AravindG
yey thx a lot
AravindG
  • AravindG
do post here if u get better attempts on the qns we skipped
AccessDenied
  • 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
  • AravindG
help
anonymous
  • anonymous
Any other question?
AravindG
  • AravindG
HMM?u knw integration and differentiation?
anonymous
  • anonymous
No, but the type of questions u posted, I think I can solve by any other method also.
AravindG
  • AravindG
did u get the book qn?
anonymous
  • anonymous
Which one? The "Page" Question????????
AravindG
  • AravindG
ys
anonymous
  • 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
  • AravindG
nop
anonymous
  • anonymous
In that case, @AccessDenied answer is rite.
AravindG
  • AravindG
can u help with that page qn?
anonymous
  • anonymous
ok. lemme try first. i didn't read the whole post was it resolved?
AravindG
  • AravindG
no
anonymous
  • anonymous
|dw:1333355356996:dw|
AravindG
  • AravindG
cntinue
AravindG
  • AravindG
wt to do next?
anonymous
  • anonymous
|dw:1333355572827:dw|