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I once used set theory in a wedding speech, but the couple were both mathematicians, conveniently having last names beginning with A and B respectively. I wouldn't recommend it in a chat up line.
Bob
How about as a complement instead?
Congratulations!
Everything looks good up to this point:
Then I plugged in the bounds and got
You made a small mistake when plugging in the bounds.
Wait is the question really trivial or am I missing something
Derrick: 0
Ari: 0.50
Wesley: 2.10
That's probably the best answer for the question as given.
158598
Welcome to the forum.
Welcome to the forum!
Let u = sin(x) and express sin(3x) in terms of sin.
158400
265^3 = 18609625
What are your limits of integration?
If I know the coordinates of C, yes
You know x. So what's f(x)?
There are other ways of finding areas besides integration.
Hi;
I am getting:
I agree with your answer.
What answer are you getting?
Yes, a sequence does not converge if it converges to two different values (i.e. it diverges). Here, your sequence given by
has two subsequences which converge to two different values depending on whether or not n is odd or even.You can try constructing a proof by contradiction of what happens when you suppose a sequence converges to two different limits.
Correct. You should be able to complete the problem now, with your answer of the form you wrote in your original post.
It seems that you can't get anything helpful from the limits of integration (in particular, f-¹(π/2) isn't that helpful). So try the geometric approach, which seems much easier:
-Plot a graph of f(x).
-Look at the area you're trying to compute.
-Can you see how to integrate the inverse function without finding it explicitly? (How would you graph f-¹(x) given the graph of f(x)?)
There are two ways to do this problem: geometrically or algebraically. (The former will give you a better idea of what's going on.)
For a geometric approach, try plotting a graph of your function and looking at which parts of the picture correspond to which integrals -- in particular, the area for your inverse function.
For an algebraic approach, make a substitution like x = f(t).
For (1), you've got to show that there exists a straight line passing through each of those points. Try looking at the difference between 4i + 5j and 3i + 3j.
For (2), the body is moving 2i - 3j metres every second, i.e. it moves 4i - 6j after 2 seconds, 6i - 9j metres after 3 seconds, and so on.
For (3), since this is a two-dimensional problem, you might find it helpful to simply plot i - j in Cartesian co-ordinates.
For (4), what are the possible values of b?
For (5) (a), speed is the magnitude of the velocity vector. So what's the magnitude of i + 3j?
For (5) (b), apply what you've done in (2).
Ditto for (5) (c).
No problem, I can post the solutions to others if you would like. #6 is basically a generalisation of the method used in post #14.