# Search results

1. ### Find local maximum value

Homework Statement y=(8/5)sint + (4/5) cost - (9/5)e^(-t/2) find its local max Homework Equations The Attempt at a Solution i have differentiated it and found out dy/dx, in order to find the local max, i have to find out the value t when dy/dx=0 but i cant solve this equation
2. ### Series converge or diverge

Homework Statement summation n from 1 to inf, 1/ln(n+5) converge or diverge Homework Equations The Attempt at a Solution 1/ln(n+5) > 1/n (from n=2 to inf) and i proved that it diverges by comparison test, am i correct? i am thinking that as my prove is n from 2 to inf not from 1 to inf...
3. ### Convergence or divergence

Homework Statement ∞ ∑ tan(1/k) k=5 show that it is convergent or divergent Homework Equations The Attempt at a Solution i used ratio test, but it's equal to 1, it means no works... i used divergence test, it equals to 0, no work too... so what should i do? i dont know how to use...
4. ### Summation series

Homework Statement ∞ Σ ( x^n/ln(n+5) ) n=1 find the value of x that the above series converges Homework Equations The Attempt at a Solution i cal. it by ratio test and i found that |x|<1 but when i input (-1,1) into my webwork...it said it's wrong[/B]
5. ### Calculate lim n->inf (n^2/n!)

lim→∞ 1/ [ (1⋅2⋅3⋅⋅⋅/n)(1-1/n)] = 1/0 = inf ??
6. ### Calculate lim n->inf (n^2/n!)

why not n / [1X2X3...(n-1)]
7. ### Calculate lim n->inf (n^2/n!)

what is wrong?
8. ### Calculate lim n->inf (n^2/n!)

Homework Statement calculate lim n->inf (n^2/n!) 2. Homework Equations The Attempt at a Solution i just calculated, and i got inf as the ans... n^2/1X2X3...Xn n/1X2X3...X(n-1) 1/[(1X2X3...)/n](1-1/n) when n->inf, it will go to inf am i correct? or there is something wrong?
9. ### Integration problem

Homework Statement integrate 1/(1+e^x) dx Homework Equations The Attempt at a Solution firstly i let t=1+e^x and then i come to : integrate 1/(t^2-1) and then i put t=secx . . . but then the final ans is -1/2 ln | 2/e^x +1 | it should be 1 instead of 2, i hv checked for the steps for so...