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
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...
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...
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]
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?
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...