Recent content by gimpy

Ok well i did problems like this before but now I am having trouble with this one for some reason. Let f(x) = \frac{1}{\sqrt{x}}. Give a \delta - \epsilon proof that f(x) has a limit as x \rightarrow 4. So the defn of a limit is \forall \epsilon > 0 \exists \delta > 0 such that whenever 0...

I was actually thinking about making \epsilon = 2 but thought it was to easy. Ok so thanks for explaining the question a bit more to me, i understand it now. :smile:

Im having a little trouble with this question. If f is continuous at c and f(c) < 5, prove that there exists a \delta > 0 such that f(x) < 7 for all x \in (c - \delta , c + \delta) So we are given that f is continuous at c. So \lim_{x \to c}f(x) = f(c) < 5 \forall \epsilon > 0 \exists...

Ok i just want to comfirm that i did this correctly. I am making a simulator for a missile launch (simple java program). Anyways the Launch pad is located at 0m and the target is located 250m away and it is 170m high and flat and infinitly long. Now i want the missile to just display where it...

Hi, I am having a little trouble with this proof: Let n be a positive integer. What is the largest binomial coefficient C(n,r) where r is a nonnegative integer less than or equal to n? Prove your answer is correct. So let r = \lfloor{\frac{n}{2}\rfloor} or r = \lceil{\frac{n}{2}\rceil}...

Thanks for your reply, Well i understand that. That was actually one of the questions which i got. Say for: (a) Full House (one pair and one triple of cards with the same face value). there are 13 different three of a kind that you can get just like 4 of a kind. Then you are left with 49...

I think my brain is freezing. I can't see how to get the answers to these questions. A poker hand is defined as drawing 5 cards at random without replacement from a deck of 52 playing cards. Find the probability of each of the following poker hands. (a) Full House (one pair and one triple...

Yes, multiple objects can fit into a box. I think my answer is correct, isn't it?

I think i got this answer. How many ways are there to distribute five distinguishable objects into three indistinguishable boxes? Wouldn't the answer just be C(5,3) because the boxes are indistinguishable? Or do i treat this question the same as if the boxes were distinguishable?

I am having trouble with this question. Let X equal the number of flips of a fair coin that are required to observe the same face on consecutive flips. (a) Find the p.m.f. of X. if found the p.m.f. to be f(x) = (\frac{1}{2})^{x-1} for x=2,3,4,... (b) Give the values of the mean, variance...

Yeah ok, i guess i am just working with integers, if i wasn't then gcd wouldn't make sense right? But why does it say that 0 \leq x \leq n/2, can't x be any real number? And when you subtract n-x wouldn't this be any real number and not an integer depending on what value x is? Or is it that i am...

Ok I am trying to solve this question. Assume n \geq 3, prove that gcd(x, n) = gcd(n-x, n) for all 0 \leq x \leq n/2. This is what i got: x = 0 then gcd(0, n) = gcd(n-0, n) = n x = n/2 then gcd(n/2, n) = gcd(n-n/2, n) = n/2 0 < x < n/2 then x = n/k for some k>2 gcd(n/k, kn/k)...

Ok i had a good nights sleep went to school and came back tonight with a fresh mind to give it another shot. And i believe it worked :D 1) Show that if f(x) \leq 0 and \lim_{x->a} f(x) = l, then l \leq 0. \forall\epsilon > 0, \exists\delta > 0 \ni for all x , 0< |x - a| < \delta, then...

I have been working ont he second question: 2) If f(x) \leq g(x) for all x, then \lim_{x->a} f(x) \leq \lim_{x->a} g(x). If those limits exist. Suppose that f(x) \leq g(x). Let h(x) = g(x)-f(x). So h(x) \geq 0. \lim_{x->a} h(x) = \lim_{x->a} g(x) - \lim_{x->a} f(x) \geq 0. Therefore...

Hi, I am taking my first analysis course and we are studying Limits right now. My prof said they are the most important thing to remember out of this whole semester. Anyways i have two problems I am trying to solve that i could do with some help. 1) Show that if f(x) \leq 0 and \lim_{x->a}...