Tagged Questions
0
votes
2answers
72 views
True/false question: limit of absolute function
I have this true/false question that I think is true because I can not really find a counterexample but I find it hard to really prove it. I tried with the regular epsilon/delta definition of a limit ...
0
votes
2answers
136 views
absolute value inequality limit
Could someone verify this proof? Prove $\lim\limits_{n\to\infty} C_n = \lim\limits_{n\to\infty} \dfrac{4n+3}{7n-5} = \dfrac{4}{7}$
Proof: Let $\epsilon > 0$ and take $N = \dfrac{41}{49\epsilon} + ...
2
votes
3answers
201 views
absolute value limit definition
For some reason, I have trouble getting absolute value right... This is of a great importance in the definition of the limit. Anyway how do I solve the following inequality for x:
$|x -a| < ...
1
vote
1answer
2k views
Limit with absolute value
I found this limit within the Calculus Single Variable book from Thomas.
$$ \lim _{x \to -2^-} (x+3) \frac{|x+2|}{(x+2)}$$
This is how I'm trying:
First of all, we need to found where the absolute ...
2
votes
3answers
321 views
Trouble with absolute value in limit proof
As usual, I'm having trouble, not with the calculus, but the algebra. I'm using Calculus, 9th ed. by Larson and Edwards, which is somewhat known for racing through examples with little explanation of ...
3
votes
1answer
174 views
Is the book wrong about this left-hand limit with absolute value? (But, my delta depends on x.)
The book says that $$\lim_{x \rightarrow 0^{-}} \left( \frac{1}{x} - \frac{1}{|x|} \right) \mbox{does not exist}$$
But, given any $M \lt 0$ of large magnitude, if I choose $\delta = \frac{-x^{2}M}{2}$ ...
