Hello all,
I am trying to solve this problem:
r balls are randomly assigned into n urns. The assignment is random and the balls are cannot be distinguished. What is the probability that exactly m urns will contain exactly k balls each ?
I know that the probability of each ball to be in each...
Hello all,
In the attached picture there is an equation. I need to fill the general expression on the left hand side, and to prove by induction that the sum is equal to the expression in the right hand side.
I am not sure how to find the general expression. Can you kindly assist ?
Thank you !
Dear all,
The function f(x) is defined below:
\[\left \{ \begin{matrix} 3x^{2} &x\leq 1 \\ ax+b & x>1 \end{matrix} \right.\]
I want to find for which values of a and b the function is differential at x = 1.
The test I was given, is to check the continuity of both f(x) and f'(x). This is...
Hello,
I got a very basic question...
A number n is dividable by 15 and 18. Can I assume from that that it is dividable by 27?
(dividable - you can divide it by 15 and get no reminder).
If it is dividable by 15, it is by 3 and 5. If by 18, it is dividable by 3 and 6, which means 3 and 2...
Hello all,
I am trying to solve a limit:
\[\lim_{x\rightarrow 0}\frac{sinh (x)}{x}\]
I found many suggestions online, from complex numbers to Taylor approximations.
Finally I found a reasonable solution, but one move there doesn't make sense to me.
I am attaching a picture:
I have marked...
Hello everyone,
I want to calculate the following limits:
\[\lim_{x\rightarrow \infty }\frac{[x\cdot a]}{x}\]
using the sandwich rule, where [xa] is the integer part function defined here:
Integer Part -- from Wolfram MathWorld
I am not sure how to approach this. Any assistance will be...
Dear all,
I am trying to prove a simple thing, that if AxA = BxB then A=B.
The intuition is clear to me. If a pair (x,y) belongs to AxA it means that x is in A and y is in A. If a pair (x,y) belongs to BxB it means that x is in B and y is in B. If the sets of all pairs are equal, it means...
Dear all,
I have two small questions regarding operations on sets.
(1) Prove that \[A\subseteq B\subseteq C\] if and only if \[A\cup B=B\cap C\].
(2) What can you say about sets A and B if \[A\B = B\] ?
In the case of (1), I have used a Venn diagram and I understand why it is true, but...
Dear all,
Attached is a picture of a circle.
The lower tangent line is y=0.5x. The center of the circle is M(4,7) while the point A is (3,6).
I found the equation of the circle, it is:
$(x-4)^{2}+(y-7)^{2}=20$
and I wish to find the dotted tangent line. I know that it is parallel to the...
Dear all,
I am trying to solve the following limit:
\[\lim_{x\rightarrow 0}(e^{ax}+x)^{\frac{1}{x}}\]
where \[a\] is a constant.
I know that the limit is equal to \[e^{a+1}\] but not sure how to prove it.
Thank you.
Dear all,
I am trying to solve a question, and I think that something is missing.
It is given that the vectors u and v are solutions to the non-homogeneous system of equations Ax=b.
If the vector ku-3v is a solution to the same system, then:
a) k = 4
b) k = 3
c) k = 0
The correct solution...