Homework Statement
Prove: If the Limit as x goes to a of f(x)=infinity and g(x)>or equal to f(x) for all x in the reals, then limit as x goes to a of g(x) is inf
Homework Equations
using delta epsilon
The Attempt at a Solution
for all e>0 there exist a delta>0 s.t g(x)<e now using...
it is something our teacher showed us how to do, but it never seems to work for me. One more question, we (meaning you) showed the limit is equal to zero becasue 1/M <epsilon? I get confused because we let m>0. so how can the limit be =0.
[b]1. Homework Statement [/bProve
Prove: If the limit as x goes to a of f(x)=infinity, then lim as x goes to a of 1/(f(x) =0
Homework Equations
Need to show with a delta-epsilon proof
The Attempt at a Solution
using the definition, lim as x goes to a f(x)=infinity means that for any...
Homework Statement
lim as x goes to 1 from the right of 2^1/x-1=inf
Homework Equations
solve using delta-epsilon
The Attempt at a Solution
i am not sure how to prove an infinite limit, I have a defn that states, If for epsilon>0 there exists an M>0 such that x>M implies...
the limit is 0, I think this because it given, also I know sin(1/x) is bounded by so that leaves x^2, so if I choose my epsilon to be sqrt epsilon. then when you square the x then x^2<epsilon
Right?
Homework Statement
limit as x goes to 0 of x^2 sin(1/x)=0
Homework Equations
Use delta-epsilon proof
The Attempt at a Solution
So |f(x)-L|=|x^2 sin(1/x)|=|x^2||sin(1/x)| and I know that sin(1/x) is bounded by one. I am not sure how to finish because of the x^2.
Both of these lines will intersect at the point (3,6), and you would have to make epsilon= e/2 to satisfy both functions when x is either rational or irrational.
[SOLVED] Analysis Question, I posted yesterday!
1. Homework Statement
Define f(x)=2x, x is rational and x+3 when x is irrational. Find all points where g(x) is continuous and prove continuity at these points
2. Homework Equations
From analysis homework and using the real definition of...