I know it\'s a lot, but these are all of the points that I have, and I would app
ID: 2828009 • Letter: I
Question
I know it's a lot, but these are all of the points that I have, and I would appreciate as much help as possible. I will award the one who answers the most questions, even if just two. Thank you very much!
1. Determine whether the sequence converges or diverges: {(2n + sqrt(n)) / (n^3 + sqrt(n))}
2. Does the sequence {(2/e)^(-n)}
A. Converge to 0
B. Converge to (e/2)
C. Converge to (2/e)
D. Diverge
3. Does the sequence {tan[(2*pi*n)/(1+8n)]}
A. Converge to (pi/8)
B. Converge pi
C. Converge 1
D. Diverge
4. Does the sequence {(e^n+e^-n)/(e^(2n)-1)}
A. Converge 0
B. Converge e
C. Converge e^2
D. Diverge
5. Can L'Hospital's rule be used to comput lim -> infinity (lnx/^3sqrt(x))
A. Yes
B. No
6. Can L'Hospital's rule be used to comput n -> 0 e^x/x^24
A. Yes
B. No
Explanation / Answer
1) bottom bigger power, so limit to infinit goes to 0 and it converges (to 0)
2) (2/e)^-n = (e/2)^2 , since e/2 > 1 it will diverge as it gets bigger forever.
3) powers are same inside so coefficients 2pi/8, so tan 2pi/8 = tan pi/4 = 1 , converge to 1
4) bottom bigger e^2n larger than e^n, so converge to 0
5) yes, b/c you get inf/inf when plugging in a large number.
6) no b/c eventually bottom will derive out to 0 but stop stays e^x.
Enjoy