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I need to find limit sqrt((3x-1)/(x+2)) when x->infinity
Can anyone help me please?
The answer is sqrt(3):
As x gets very very big, the degree 0 terms (-1x^0 and 2x^0) grow insignificant thus leaving:
sqrt(3x/x)
As you can see this reduces to:
sqrt(3)
And this is no longer affected by x and is, then, the answer.
Note
Math questions are best suited on Stack Exchange's Math page.
mjgpy3 deserves credit for his correct and elegant explanation.
But I'll offer you Wolfram Alpha as a way to answer these for yourself without having to ask here:
http://www.wolframalpha.com/input/?i=limit%20%20sqrt((3x-1)%2F(x%2B2))%20%20as%20x-%3Einfinity
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I've never seen this notation for complexity: Õ(n).
It comes up in the context of learning in stochastic algorithms.
Anyone know this notation? You can't exactly google this...
EDIT: SOLVED
I think people have pointed out the right answer below. In my case Õ() is used to hide an exponential growth of a tree.
It is shorthand for O(g(n) log^k g(n))
Actually, you can google this!
It is a variant of big-O that ignores logarithmic factors. See this wikipedia entry, which I found simply by googling that character and looking at the top entry.
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I am learning binary division following the step-by-step procedure. I am stuck at Step One Repeat One in the remainder section. To get the remainder, the formula is Remainder = Remainder - Divisor.
How do we get to remainder: 11100110? I just don't understand how we have 1110 on the left half of the register. Any guides or help would greatly be appreciated!
Thanks:
The example is 10/5 using an 8 bit ALU.
I have attached a picture of the example for reference
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I know that (a*b)%M = (a%M * b%M)%M
But what if the equation was :( (a*b)/c )%M ..I dont think I can use the above logic here also..And here M is a non-prime number ..You may assume that (a*b)/c will NEVER end up in a floating value..
For eg:
If a=10 b=9 and c=6,M=4 then (a*b)/c=15 and 15%4=3
but if I use the property as it is with multiplications then ((10%4*9%4)/(6%4))%4= (2*1)/2=1
Please tell me how to solve this kind of problem??
If c and M were relatively prime, you could multiply c^-1%M and the math should work. However, if GCD(c,M)>1, then c^-1%M doesn't exist, and there is no easy way to do it that I know of.
As far as what c^-1%M is, its the number such that c*c^-1%M=1. For example, if c=2 and M=9, 2*5%9=10%9=1, so c^-1%M=5.
You can calculate c^-1%M with the extended euclidean algorithm -- you get ac+bM=1, so ac=1+(-b)M and ac%M=1.
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In how many different ways can a cube be painted by using three different colors of paint?
The answer of this is 45,
What if I change cube to cuboid?
Thanks!
I am preparing for job interview and this question is from CareeCup.
First, you should know how 45 is derived. That is by the use of permutation and combination.
Since a cuboid has the same number of sides as a cube, they should have the same answer. So the answer is 45.
But it is important to learn how the 45 is derived.
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I know it's not programming question but I thought we could all use the challenge :)
Link to diagram
Point A is the source of a laser. It is shinned at a single mirror and then reflected to another mirror finally arriving at point B ... see picture.
The goal is to find the total distance of all the lines.
I am not a student and this is not homework.
Same as a straight line from (-x, y) to (a, -b).
sqrt((a+x)^2 + (b+y)^2)