1. Homework Statement
Let $$(a_n)$$ be a sequence such that $$\lim_{n\rightarrow +\infty}n(a_n)=0$$.
1) What is
$$\lim_{n\rightarrow +\infty}(1 + {\frac{1}{n}} + (a_n))^n$$
2) For which value of p and l, after some n is $$(b_n)=\frac{n^{p \ cos(n\pi)}}{(1 + l + (a_n))^n}$$ properly...
1. Homework Statement
Let f: R -> R and defined with f(x)={ x, if x \in Q or x^2 if \in R\Q}
a) Prove that function is discontinuous at x=2;
b) Find all points for R in which function is continuous;
3. The Attempt at a Solution
As far as i know there are infinitely many irrationals but...
Theorem: Suppose S is an ordered set with the least-upper-bound property, B⊂S, B is not empty, and B is bounded below. Let L be the set of all lower bounds of B. Then α=supL exists in S, and α=infB.
Rudin proves that α=supL, α is an element of L and that α=infB.
For α to be sup i.e. lub it...
1. Homework Statement
If p is a prime and k is an integer for which 0<k<p, then p divides \displaystyle \ \binom{p}{k}.
Whne p divides \displaystyle \ \binom{p}{k} it means that \displaystyle \ \binom{p}{k}=p*b.
wheren b is some number.
3. The Attempt at a Solution
So p is equal to some...
The question was: How many real number solutions are there for 2^x=-x^2-2x. I tired for an hour to isolate x but i couldn't do it. Then i used wolfram alpha and it gave me two solutions and graph. I realized that question was, how many not what are the solutions, and i could do that by graphing...
1. Homework Statement
Numbers a,b,c are consecutive members of increasing arithmetic progression, and numbers a,b,c+1 are consecutive members of geometric progression. If a+b+c=18 then a^2 +b^2 + c^2=?
3. The Attempt at a Solution
a + b + c= 18
a + a +d +a + 2d = 18
3a + 3d = 18
3(a+d)=...
1. Homework Statement
If a,b,c, are at the same time fifth, seventh and thirty seventh member of arithmetic and geometric progression then a^{b-c}b^{c-a}c^{a-b} is:
3. The Attempt at a Solution
I tried solving system of equations but i have four unknown. I was able to reduce it to on...
1. Homework Statement
Let X be a set containing all four digit numbers made up of {1,2,3}, where every number contains every digit at lease once. Number of all subsets is:
3. The Attempt at a Solution
So firs i have to find number of elements in the set:
3!*3 + 3*12 = 54
Now what...
In October of this year i will start with math major and i decided to prepare myself in spear time. In my faculty there is no such thing as Calculus but rather you go strait to the analysis and you pick up calculus along. (There is singe variable calculus in high school). In first two years...
Is there planned research that tries to create new organ for transplantation? So when someone needs a new organ e.g. kidney, instead of finding a donor, scientists could create an organ form stem cells perhaps. Is this even psychically possible?
Reason i ask this question is that i watched...
1. Homework Statement
Find the equation of a cricle if it touches x axis in A(3,0) and it contains B(3 + √3, -1)
3. The Attempt at a Solution
Is there a piece of data missing here? Because i cant see how can i find center of circle.
1. Homework Statement
Prove the following:
\frac{n!}{m!(n-m)!} = \frac{n!}{(m-2)!(n-m + 2)!} + 2* \frac{(n-1)!}{(m-1)!(n-m)!} + \frac{(n-2)!}{(m-2)!(n-m)!}
3. The Attempt at a Solution
I tried writing following
\frac{n!}{m!(n-m)!} = \frac{n!}{m!(n-m)!}(\frac{m(m-1)}{(n-m +...
1. Homework Statement
1.) 4 of the books have red covers, 3 have green covers, and another 2 have gray covers. In how many ways can the books be arranged on a shelf if books of the same color must be arranged together?
3. The Attempt at a Solution
1) I think that the answer here is...
1. Homework Statement
Find parameter a so that line y=ax + 11 touches ellipse 3x^2 + 2y^2 = 11
3. The Attempt at a Solution |
I can rewrite ellipse equation like \frac{x^2}{\frac{11}{3}} + \frac{y^2}{\frac{11}{2}} = 1
And i know that line y=kx + n touches ellipse when a^2k^2 + b^2 =...
1. Homework Statement
Show that \frac{a+b}{2}\geq\sqrt{ab} for 0 < a \leq b
3. The Attempt at a Solution
Since b \geq a then b + a \geq 2a and 2b\geq a + b
That is \frac{a+b}{2}\geq a and \frac{a+b}{2}\leq b.
Since \frac{a+b}{2}\leq b can i multiply \frac{a+b}{2}\geq a with...
1. Homework Statement
Integrate \int3^x\cos x\,dx
3. The Attempt at a Solution
It has to be done using partial integration.
I don't know what should be u?
Hello friends.
It seems to me that i have reach a wall with my math education. In 3.5 months i will be doing tests for mathematics faculty(college), something like SAT but a bit more difficult i think.
Anyway i have been doing more difficult problems from problem set and i simply cant figure...
1. Homework Statement
I should sketch function (x^2 + x -12)/(x-4).
3. The Attempt at a Solution
I have problem with first derivative i find it to be (x^2 - 8x +8)/(x-4)^2 with roots at 4 - 2√2, 4 + 2√2, and 4(we lose four because f is not defined at 4). Where at 4 - 2√2 f is at...
I have been using physics forum for good year and a half now for homework problems and for asking for advice, so i wanted to subscribe but it is only possible to do it over paypal, but in Serbia where i live we don't have paypal so i can't do it. Is there any other way to subscribe and if not it...
Hi everybody,
i didn't wanted to create two separate threads so merged them into one.
i got confused watching Brian Green explaining QM on one of his shows.
He compared distribution in double slit experiments with throwing a ball on a roulette.
He said that casino doesn't have to know...
1. Homework Statement
Let f be defined for all real x and suppose that,
\left|f(x) - f(y)\right|\leq(x-y)^2
for all real x and y. Prove that f is constant.
3. The Attempt at a Solution
First of all, is following allowed. Since f is constant then \left|f(x) - f(y)\right|=0, and form here to...
1. Homework Statement
Of all cylinders inscribed in sphere of radius R largest area of side(M) has cylinder which hight is R\sqrt{2}. Prove.
3. The Attempt at a Solution
I understand how to prove this i only have problem with derivative:
M=2*r*Pi*H and r=\frac{\sqrt{(2R)^2 - H^2}}{2}...
1. Homework Statement
Sum of first three members of increasing arithmetic progression is 30 and sum of their squares is 692. What is the sum of the first 15 members?
3. The Attempt at a Solution
So i have system of equations:
a1 + a2 + a3 = 30
(a1)^2 + (a2^2) + (a3^2) = 692...
1. Homework Statement
Let a_{m+n}=A and a_{m-n}=B be members of arithmetic progression then a_{m} and a_{n} are? (m>n).
3. The Attempt at a Solution
I fugured that a_{m}=\frac{A+B}{2} but i have no idea what a_{n} is.
In my text book solution is a_{n}=\frac{(2n-m)A + mB}{2}
How did they...
1. Homework Statement
Find the first derivative of (5/x)+(5/SQRT(x))
2. Homework Equations
Derivative ruls
3. The Attempt at a Solution
Is this correct? Thank you
1. Homework Statement
Show that function is even or odd:
(x^2|x-1|)/(SQRT(x-1)^2)
2. Homework Equations
3. The Attempt at a Solution
(-x^2|-x-1|)/(SQRT(-x-1)^2)
After this i dont know how to procede.
Hi everyone, i dint post this i homework section because i know how to solve the problem.
So here is a problem
So i am standing and in my own reference system S i observe two objects moving toward each other at speed 2*10^5 km/s each. Object in it's own reference system S' is observing object...
1. Homework Statement
I took this form Yale Open Course
2. Homework Equations
Special Relativity equations
3. The Attempt at a Solution
I will try to divided this problem into two parts: First one is - what is its location
in my frame when it ticks 1 second in its frame? and...
I am doing exercises form Velleman's How to Prove It
1. Homework Statement
1. Suppose a and b are real numbers. Prove that if a < b < 0 then a^2 > b^2.
2. Suppose a and b are real numbers. Prove that if 0 < a < b then 1/b < 1/a.
3. Suppose a and b are real numbers. Prove that if a < b...