Homework Statement
I was reading my textbook and i encountered this...--->>
" For instance if f,g,h are in A(S) and fg = fh then g=h " I understand this part... because we can take the the inverse of f both sides and say g=h.
then it says--->> " If gf = f^(-1)g but since f ≠ f^(-1)...
why can't you rewrite the the limit. example, 1/x can be rewritten as x^-1. another example (sin(x) / x )^x can be rewritten as sin(x)^x / x^x.
After that, you can use L'Hopital rule which you take the derivative of the top and the derivative of the bottom then you will plug the limit value...
Homework Statement
show for finite sets A,B,that m(A x B ) = m(A)m(B).
Homework Equations
I don't see relevant equation but we can treat to like cartesian/cross product.
The Attempt at a Solution
I tried to think it as (x,y) for m(A x B ) . if we let A = { 1,2} and B= {3,4}...
Homework Statement
Two sets A and B.
B contain al the upper bound of A.
whats is the relationship between the lub of A and the glb of B
Homework Equations
The Attempt at a Solution
I am little bit confused , help please
Additional to the question i asked,
a_{N(E)} < L - E
THEN
a_{(N(E)} < L - E < a_{n}
but we know
a_{n} >= L
THEN
L <= a_{n} <= L+E
BUT I STILL HAVE PROBLEM BECAUSE I DON'T KNOW IF a_{n} <= L+E IS TRUE.
Homework Statement
A bounded monotone sequence converges.
Proof
for bounded monotone increasing sequence and decreasing sequence.
Does both them converges?Homework Equations
So, I used the least upper bound and great lower bound to prove increasing sequence and decreasing sequence...
ok..another try...i won't stop until i get this ...
suppose a>b and let ε = 1/2 (a-b) ...(i think you know where i get that)
so a < b+ε → a< b+(1/2a-1/2b)
then a-1/2 < b-1/2 → 1/2a<1/2b→ a<b CONTRADICTION ∅
ok! so i tried it this way...
Suppose a > b+ε for every ε>0,then a≤b
let ε= 1/2a-1/2b since a-b>ε→→→a-b >1/2a-1/2b (true)
so a> b+ 1/2a-1/2b
1/2a>1/2b
a>b which contradict from the first agreement ∅
Homework Statement
Show that if a < b + ε for every ε>0 then a ≤ bHomework Equations
I am not sure if this is a right way to do it? I just want to know if it does make sense
The Attempt at a Solution
proof.
a < b + ε → if a is bounded above by b+ε then b is the least upper bound for a...
Hello
I am kinda confused when it comes to finding a general solution of equation.
Here is the question.
Y'' + 6Y' +9Y = 0
Solution
Y'' + 6Y' +9Y = 0
I used "x" instead of Lamda...ANYWAY
X^2 + 6X + 9 = 0
FACTOR IT WHICH IS (X+3) (X+3) = 0
X IS EQUAL TO -3.
HERE IS WHERE I...
Homework Statement
An electron orbits in a 5.76 mT field with an angular momentum of 6.10 x 10-26 kg m2/s. What is the radius of the orbit (in m)?
Homework Equations
F = mv2/r
F= QRB
The Attempt at a Solution
MV2/r = qrb
v = wr
so i plugged and my answer is still wrong .any help...
\sqrt{}Homework Statement
What is the escape speed (in m/s) of an electron launched from the surface of a 7.42 cm diameter glass sphere that has been charged to 7.04 nC?
Homework Equations
u=kqq/r
KE=1/2MV^2
UO=KE
The Attempt at a Solution
here is what i did
kqq/r = 1/2mv^2...
Hi
yes the answer is f(x)=1 because both of them have the highest power of n so based on that if you have the same power you just take the cofficient which is one.
x^n/x^n = 1 when the limit goes to infinity.
Homework Statement
The electric field strength 8.05 cm from a very long charged wire is 1310 N/C. What is the electric field strength (in N/C) 30.0 cm from the wire?
Homework Equations
E=F/Q
E=KQ/R^2
The Attempt at a Solution
First I try to find the charge using E=KQ/R^2...