Homework Statement
For x > 0, define y(x) := x \int_0^{log x} \! \sqrt{1 + e^t} dt -(2/3)(1 + x)^{3/2}
Calculate y'(x) := dy/dx
and
y''(x) := d^2y/dx^2
Homework Equations
The Attempt at a Solution
would like to work through this with person/people please. Not sure...
ok I get it now, we got the system of equations and we showed that (ii) holds
is the same as saying there is no solutions of the linear equations which is exactly what one says (i) ?
okay thanks, that is a lot more clear now
we will have m equations:
\alpha_1c_{1,1}+...+\alpha_nc_{1,n}=c_{1,(n+1)}
.
.
.
.
\alpha_1c_{m,1}+...+\alpha_nc_{m,n}=c_{m,(n+1)}
we assumed linear dependence, so I think we are trying to prove by counterexample
that linear...
okay I think I understand a bit better, so considering c1 this will form the
first colum of A and it will have m rows, so we will have these equations, for the first row
of A it will be
c11c1 + c21c2 + ... + cn1cn = c(n+1)1
were cij s.t. i=column j=row
and the second...
Okay I think perhaps from this information I could get
a_1c_1 = c_{n+1} - a_2c_2 - a_3c_3 - ... - a_nc_n
and then do this for c_2 ... c_n and have n equations
but I'm not sure how we would get a system of m equations from this,
unles we made a matrix with m rows. Also I see the...
Homework Statement
If we let A be the augmented m x (n + 1) matrix of a system of m linear equations
with n unknowns
Let B be the m x n matrix obtained from A by removing the last
column.
Let C be the matrix in row reduced form obtained from A by elementary
row operations...
Is this statement true or false
if false a counterexample is needed
if true then an explanation
If T : U \rightarrow V is a linear map, then Rank(T) \leq (dim(U) + dim(V ))/2
For a fixed y \in R , if
f(x) = [sin(x+y)]-(sin x) (cos y) − (cos x) (sin y)and we let E(x) = [f(x)]^2+[f'(x)]^2.
How do we prove the addition formulae for sin(x + y)and cos(x + y) by applying the Mean Value Theorem to E
so I did the following:
\dfrac{|f(y) - f(x)|}{|y-x|}\leqslant |y-x|
was obtained by (y-x)^2=|y-x||y-x| and dividing both sides by |y-x|.
then trying to use the fact that
\displaystyle\lim_{y\to x}\frac{f(y)-f(x)}{y-x} is the derivative at x
but not sure what's next how to...