Which of the following functions is odd? and why?
828998
odd functions:\nf-x) = -f(x)\ng(-x) =2sin(-x)cos(-x)tan^2(-x)\n\nnow sin(-x) = -sinx\ncos(-x)=cosx\ntan(-x)=tanx\nso g(-x) = -2sinxcosxtan^2x=-g(x)\nodd function\n\nsimilarly do otherr fns\n\nalso graphically if you plot these fns they are antisymmetric wrt zero on coordinate plane\n\nif f(-x) =f(x) then it is evn fn.\nwhile if f(-x) is neither + nor - f(x) but a different function then it is neither odd nor even likes(x)
500368
The links below have good info. The first briefly addresses your first question, and the second is a good brief history of the problem which provides some insight as to the difficulties encountered. I actually played around with this problem a little on an elementary level and it is interesting. Cheers.\n\nhttp://www.sciam.com/print_version.cfm?articleID=000DBA55-B698-1C71-9EB7809EC588F2D7\n\nhttp://www.geocities.com/fermatnow/flt/
312174
It seems undefined since for x <= 0 and x != odd number, x^x doesn't work out so well.  If it's x->0+, then it's just 1.
90715
neither, the terms even and odd refer to integer numbers, not decimal or fractional ones.\n\nhope this helps :-)
120442
Because of the way you would call the function \nsomefunct(param1, param2, param3); // canonical\nsomefunct(param1, param2); // compiler knows you mean to use the default param for 3 because it´s the third param you don´t provide.
747397
Checking by method of differences\n\n. x ............. f(x) ...... Δ1 ...... Δ2\n. 0 .......... 1104\n. 1 .......... 1104 ........ 0\n. 2 .......... 1100 ........ 4 ....... -4\n. 3 .......... 1092 ........ 8 ....... -4\n. 4 .......... 1080 ...... 12 ....... -4\n. 5 .......... 1064 ...... 16 ....... -4\n. 6 .......... 1044 ...... 20 ....... -4\n. 7 .......... 1020 ...... 24 ....... -4\n. 8 ............ 992 ...... 28 ....... -4\n. 9 ............ 960 ...... 32 ....... -4\n10 ............ 924 ...... 36 ....... -4\n11 ............ 884 ...... 40 ....... -4\n12 ............ 840 ...... 44 ....... -4\n13 ............ 792 ...... 48 ....... -4\n14 ............ 740 ...... 52 ....... -4\n15 ............ 684 ...... 56 ....... -4\n16 ............ 624 ...... 60 ....... -4\n17 ............ 560 ...... 64 ....... -4\n18 ............ 492 ...... 68 ....... -4\n19 ............ 420 ...... 72 ....... -4\n20 ............ 344 ...... 76 ....... -4\n21 ............ 264 ...... 80 ....... -4\n22 ............ 180 ...... 84 ....... -4\n23 .............. 92 ...... 88 ....... -4\n24 ................ 0 ...... 92 ....... -4\n\nSo the relation is quadratic (as Δ2 is constant which imples the 2nd derivative is constant)\n\nSo the relation is of the form\n\nf(x) = ax^2 + bx + c\n\nNow f(0) = c = 1104\nf(1) = a + b + c = 1104\nSo a + b + 1104 = 1104\nie a + b = 0\n\nf(2) = 4a + 2b + c = 1100\n4a + 2b + 1104 = 1100\nSo 4a + 2b = -4\n\nie 2a + 2a + 2b = 2a + 2(a + b) = -4\nSo 2a + 0 = -4\nie a = -2 and b = 2\n\nThus f(x) = -2x^2 + 2x + 1104\n= -2(x^2 - x - 552)\n= -2(x - 24)(x + 23)\n\nTest f(10) = -2*(10 - 24)(10 + 23)\n= -2 * (-14) * (33)\n= 28 * 33\n= 924 YESSSSSSSSSSS!!
948825
First answerer correct.  \n\nBut the second set is a function, because there are no repeated x values.  If you have a component of the first set corresponding to two different components of the second, then it isn't a function, e.g. in the second set, if the next pair were (15, 5) then it wouldn't be a function because of the double result for 15.  In the first set, if your misprinted pair were (1,2) then it wouldn't be a function, same reason.
784978
Depends on what calculator you use...some are +/- and some are just -. So it depends...Sometimes you have to push 2nd function to get it.
1013129
Please explain what is ~f.  I have curiosity, because neither inverse multiplicative, complex conjugate or inverse function could do that result...\n\nIt should be interesting!! Please post what is ~f !
780058
If definition of odd function is like this: y=f(x) then f(-x)=-y. Thus your integral should be = 0 as a result of definition above. The odd function has polar symmetry – the [0, 0], while even function is symmetrical with OY-axis. Examples: y=x^2 is even, y=x^3 is odd, y=e^x is neither
90357
F- even and odds.  There are 3 even sides and 3 odd sides. So the likelihood is the same for both.
810128
Neither.\n0/0 is indeterminate, or undefined.
1133182
that they are weird, or odd.
894070
all the questions relate to the same basic problem. When a function p(x) changes sign in the interval [a,b] it has to cross the real line (y=0). Therefore it has a real solution there. So, first question is solved since p(1) is negative and p(2) is positive.\n\nthe second question has the same answer, only more complicated but just a change of sign when you consider the polynomial function f(x) - g(x).\n\nthird. all non-real solutions come in pairs therefore an odd degree polynomial has at least one real solution since the number of solutions equals the number of roots. (Fundamental theorem of algebra.)
324897
Could be 10,14,13. The odd terms differ by 3 (eg. 4-1,7-4), the even terms differ by 4.
1148883
I assume what looks 'funny' to you is the wild oscillations near x=0.  The reason is that for x near zero, the quantity 1/x gets really large, and as x gets closer to zero the value of 1/x changes a LOT for a small change in x.  What this means for sin(1/x) is that the sine function goes through many oscillations over just a small range of x (near zero) because its argument changes so much.  Does that make sense?\n\nSee if you can make an argument for what behavior to expect for sin (1/x) when x is far from zero instead (positive or negative).
662739
a function is like a machine. when u input a no into it..it gives u a product corresponding to that no. now two or more different inputs can generate the same product from the machine. it only means that the machine recognizes a special characteristic of THAT group of inputs and generates the output not according to the individual no but according to that special characteristic of that group of inputs. for example sin 0=0 also sin 360=0 also sin 720=0...here sin is the machine which takes the inputs as 0,360,720..and gives the result as  0...the common characteristic of this group of inputs is that all of them can be represented as 2n(360) where n is any integer...the sin function recognizes this characteristic and generates the result accordingly