Recent content by Yankel

I tried proving this by induction using the general statement that skeeter wrote, but I couldn't do it. I am stuck at the n=k+1 stage...

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...

Great idea... so the correct answer is the constant a then ? If x goes to infinity, 1/x goes to 0

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...

I am sorry, I did not mention this. The problem is in analytical geometry, no vectors are allowed

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.

So are you saying that k can't be 3 ?

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...

Oh...silly me. x-y = 0 and z=0. So V is also a subspace, has to be then.