The trouble with multivariable limits is that there are literally infinitely many paths one can take to approach the limit point. Showing that a given limit exists means finding a systematic proof to...
Type: Posts; User: ksdhart2
The trouble with multivariable limits is that there are literally infinitely many paths one can take to approach the limit point. Showing that a given limit exists means finding a systematic proof to...
Whoops! Yes, I missed a minus sign out front of the whole thing. It should really be -\dfrac{2(t^2-1)}{(1+t^2)^2}. Flipping the order of the terms in the numerator would achieve the same effect....
The catch is that you've changed the variable. It's true that \dfrac{d(sin(x))}{dx} = \dfrac{d}{dx} \left( \dfrac{2t}{1+t^2} \right) = \dfrac{1-t^2}{1+t^2} = cos(x). However, \dfrac{d(sin(x))}{dt} =...
Personally, I think the question is a bit poorly written and ambiguous. If we interpret it to mean "Find the probability that a card drawn at random will be both red and black," then you're correct...
But what are your thoughts? What have you tried? Please re-read the Read Before Posting thread that's stickied at the top of each subforum and comply with the rules found within. Particularly, please...
Very good! The only minor criticism I have is that you're missing some grouping symbols. For now, it's clear what you meant from context, but in the future it may not be as clear and could result in...
Oh, hey, sorry about the delay. For some reason I didn't get notified of your response. If I hadn't happened to manually check out of curiosity, it may have gone forever unnoticed. I'll have to...
Well, you say you can't reproduce the answer, which directly implies you've tried at least one method. That's excellent! Trying things is usually the best way to learn. Unfortunately, we cannot...
A good place to start is to refresh yourself with the definition of logarithm. The definition means that if b^y=x then log_{b}(y)=x. Perhaps consider a few concrete examples. 2^3 = 8 implies that...
Everything you did is fine, up to this point:
\dfrac{8(x-2)-x(x^2-4)}{(x^2-4)(x-2)}
In the next step, you made an error when expanding the denominator. This is what you should have gotten:
...
Unfortunately, what you're seeking is not possible. Consider the data set {118, 119, 119, 137, 137, 137, 140, 140, 140, 155, 155, 160, 160, 173, 173, 173, 191, 191, 200}. This meets all of your...
Oh dear. I seem to have majorly messed up here. Sorry about that. Upon further reflection I see now that my proposed solution of 730 would only be valid if the balls were in some way distinguishable...
It's not immediately obvious what you mean by "1st one," but I'll guess that you probably mean part (1a). Assuming that's the case, your proposed answer is not correct. Since you've not shown any...
Those sure are some very nice homework problems you have there. But what are your thoughts? What have you tried? Please re-read the Read Before Posting thread that's stickied at the top of each...
From my perspective, it looks like your main problem isn't really that you're "bad at probability" or even bad at math. Rather, the problem is that you don't have a clearly defined problem. I'll be...
Your only flaw here is that you've subjected yourself to rounding errors. 199/98 is not exactly equal to 2.03061224, and neither is 5/98 exactly equal to 0.05263158. As far as I can tell, there's no...
Those sure are some very nice homework problems you have there. But given that this is a tutoring website (note that the name is "Free Math Help," not "Free Homework Solutions" :p), we'd like to see...
The reason why you can't use the binomial formula here is that it only works if the probability of each event is constant. That's not the case here. You've correctly identified that the probability...
Often times when I'm stuck on a math problem, I find it immensely helpful to consider a smaller/simpler version of the problem, to help me get a feel for what's going on. Then I can attempt to scale...
Truthfully, I'm not really sure what more you want in order to consider it a "professional" solution/explanation. The problem asks you to explain why there's at least one solution, and you've done...
It seems to me like all of your work so far has been focused solely on trying to find a common difference between the terms, to which end you've discovered there doesn't appear to be any such...
What you've done so far is fine, and if you continue to simplify and evaluate the limit you will get the correct answer. But I think it would be way easier to differentiate first, and then plug in...
Actually, Denis, the problem text specifically instructed OP to "find x," directly implying that they were meant to come up with a numerical solution rather than an expression in x.
I can infer from context that you've not shown any work because you're stuck at the very beginning and have none to show. That's perfectly alright. The key words to pick out of the problem text are...
As it turns out, there's four unique solutions to this problem. You identified one such solution, which should suffice (although I have seen teachers refuse to accept any answer except their...