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need help!
alright, the first q is on integration technics.
1) f(x) = 16 + 2x + 15x^2 / (1+x^2)(2-x) = A+BX / (1+x^2) + C/ (2-x)
A=0 B=1 and C=16 to give
f(x) = 16 + 2x + 15x^2 / (1+x^2)(2-x) = X / (1+x^2) + 16/ (2-x)
next i had to integrate it between 1 and 0 and got 33/2 ln2
the next part is where i need the help. i dont really understand what its asking for
.
Express f(x) as a sum of powers of x up to and including x^4. determine the range of values of x for which this expansion of f(x) is valid
the next q is about max and min values
2) i got parametric equations of:
x=2cos(theta) + sin (theta)
y= cos (theta) + 2sin (theta)
for 0 </=x<2pi
i had to express x in the form R cos (theta-alpha): ans= root5 cos (theta - 0.4636)
next i had to find the graient ar point where theta= pi/2 ans=0.5
then i had to show x^2 + y^2 =5 + 4sin2 theta which i did.
i had a go at this but couldnt do it.
Find the greatest and least distances of a point on the curve from the origin.
i had a go at differentiating it again...but that didnt work, but i just noticed i used the values 0 and 2pi. but i failed on that, i couldnt thonk of anything else.
1) f(x) = 16 + 2x + 15x^2 / (1+x^2)(2-x) = A+BX / (1+x^2) + C/ (2-x)
A=0 B=1 and C=16 to give
f(x) = 16 + 2x + 15x^2 / (1+x^2)(2-x) = X / (1+x^2) + 16/ (2-x)
next i had to integrate it between 1 and 0 and got 33/2 ln2
the next part is where i need the help. i dont really understand what its asking for
.Express f(x) as a sum of powers of x up to and including x^4. determine the range of values of x for which this expansion of f(x) is valid
the next q is about max and min values
2) i got parametric equations of:
x=2cos(theta) + sin (theta)
y= cos (theta) + 2sin (theta)
for 0 </=x<2pi
i had to express x in the form R cos (theta-alpha): ans= root5 cos (theta - 0.4636)
next i had to find the graient ar point where theta= pi/2 ans=0.5
then i had to show x^2 + y^2 =5 + 4sin2 theta which i did.
i had a go at this but couldnt do it.
Find the greatest and least distances of a point on the curve from the origin.
i had a go at differentiating it again...but that didnt work, but i just noticed i used the values 0 and 2pi. but i failed on that, i couldnt thonk of anything else.
Sorry OP, this is off-topic, but bobo - you're in Year 11 and you're going to do STEP III?
*bobo*
yes, i'm ready to do them so theres no point in waiting till a 2 years time when the topics covered won't be fresh in my mind
fookin hell, that's amazing. Good luck
IsOLaTiOnIsT
next i had to integrate it between 1 and 0 and got 33/2 ln2
f(x) = (16+2x+15x^2)/(1+x^2)(2-x)
......= (A+Bx)/(1+x^2) + C/(2-x)
(16+2x+15x^2) = (A+Bx)(2-x) + C(1+x^2)
(16+2x+15x^2) = (2A+2Bx-Ax-Bx^2+C+Cx^2), so 2A+C = 16, 2B-A = 2, C-B = 15
B = 1, A = 0, C = 16
f(x) = x/(1+x^2) + 16/(2-x)
INT f(x).dx [from 0 to 1]
= INT x/(1+x^2) + 16/(2-x).dx [from 0 to 1]
= (1/2) INT 2x/(1+x^2).dx - 16 INT -1/(2-x).dx [from 0 to 1]
= [(1/2)ln(1+x^2) - 16ln(2-x)] [from 0 to 1]
= (1/2)ln(1+1^2) - 16ln(2-1) - (1/2)ln1 + 16ln2
= (1/2)ln(2) + 16ln2
= (33/2)ln(2)
*bobo*
1)use maclaurin series
differentiate f(x) and then f'(x) and f''(x) etc
find the values for these when x=0
f(x)=f(0)+ f'(0)x + (f''(0)x^2)/2! + ....
2)x=rcostheta, y= rsintheta
r^2= 5+4sin 2theta
r= (5+4sin 2theta)^0.5
dr/dtheta= 4cos 2theta/(5+4sin2theta)^0.5
dr/dtheta= 0 for max and min r
differentiate f(x) and then f'(x) and f''(x) etc
find the values for these when x=0
f(x)=f(0)+ f'(0)x + (f''(0)x^2)/2! + ....
2)x=rcostheta, y= rsintheta
r^2= 5+4sin 2theta
r= (5+4sin 2theta)^0.5
dr/dtheta= 4cos 2theta/(5+4sin2theta)^0.5
dr/dtheta= 0 for max and min r
year 11 doing STEPS :O....i wish i had a brighter mind 
...well done on u, hope u do well 
oh thanx for the help to who ever contributed 
...well done on u, hope u do well oh thanx for the help to who ever contributed *bobo*
2)x=rcostheta, y= rsintheta
r^2= 5+4sin 2theta
r= (5+4sin 2theta)^0.5
dr/dtheta= 4cos 2theta/(5+4sin2theta)^0.5
dr/dtheta= 0 for max and min r
2)x=rcostheta, y= rsintheta
r^2= 5+4sin 2theta
r= (5+4sin 2theta)^0.5
dr/dtheta= 4cos 2theta/(5+4sin2theta)^0.5
dr/dtheta= 0 for max and min r
shout at me if im wrong, but if ur differentiating, isn't the power ment to decrease by one and times it by new power
.......i feel so stupid thanx again
thanx againjust reading what u suggested for q1) ive never come across ur method, im guessing binomial is the other option, right?
IsOLaTiOnIsT
just reading what u suggested for q1) ive never come across ur method, im guessing binomial is the other option, right?
(In fact, if you do it by Maclaurin expansion, I don't see how you are supposed to give the range for which the expansion is valid, at least within the confines of the A-level syllabus).
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