Homework Statement
Use the binomial series to expand the function as a power series.
1/(2+x)3
I have attached an image. I understand until the end of the second line. I don't see the reasoning used to follow through to the third line. the (-1)^n is because the sign alternates becoming...
Homework Statement
∫arctan(√x)dx.
Using the substitution √x=t:
∫arctan(√x)dx = ∫arctan(t)dt2
This is what I've got written in a solution manual. I don't see why the dt would be squared. Could anyone care explaining me? thanks
By the ratio test I'm left with: 2 x limx->\infty |nn/(n+1)n+1)| which is the same as what i previously wrote: 2 x limx->\infty [n/(n+1)]n*1/(n+1).
Dividing by the largest power of the polynomial in the denominator:
2 x limx->\infty [1/(1+1/n)]n*1/(n+1).-
so it becomes: 2 x limx->\infty...
Homework Statement
\sum ftom n=1 to \infty (-2)n/nn.
The Attempt at a Solution
limn->\infty | (-2)n+1/(n+1)n+1) x nn/(-2)n | = |-2|limn->\infty |(n/n+1)n*(1/n+1) |
If it were only (n/n+1) then would the answer be 2e? Either way, how do you sole this the way it is?
Homework Statement
(2x+3x)/6x = 2-x+3-x
I've tried moving the 6 above, splitting it up and so... but i can't figure how to do it. It must be pretty simple, but I am just not seeing it. all helps appreciated!
Without knowing about the form of the complementary solution at first, we'd figure that if G(x)=x2ekx then the particular solution should be something like this: (Ax2+Bx+c)ekx?? And say that you then worked out the complementary solution and it was: c1er1x+c2er1x, then the last term "c"...
Homework Statement
y''+2y'+y=xe-x
Homework Equations
Yc=c1e-x+c2xe-x
relevant info on textbook: "If any term of yp is a solution of the complementary equation, multiply yp by x (or by x2 if necessary)."
>> i don't understand the part where it says "a solution of the complementary equation"...