Continuous function proof by definition Ask Question Asked 12 years, 8 months ago Modified 6 years, 6 months ago

As you have it written now, you still have to show $\sqrt {x}$ is continuous on $ [0,a)$, but you are on the right track. As @user40615 alludes to above, showing the function is continuous at each point in the …

A function is "differentiable" if it has a derivative. A function is "continuous" if it has no sudden jumps in it. Until today, I thought these were merely two equivalent definitions of the same c...

A function is called uniformly continuous if you can prove that given epsilon, the required value of delta depends on epsilon but NOT c. 1/x is NOT uniformly continuous on (0,1) which is why you can't get …

Clearly if $f$ is continuous then its kernel is closed set. for the converse, assume that $f\neq0$ and that $f^ {-1} (\ {0\})$ is a closed set. Pick some $e$ in $X$ with $f (e)=1$.

12 Following is the formula to calculate continuous compounding A = P e^(RT) Continuous Compound Interest Formula where, P = principal amount (initial investment) r = annual interest rate (as a …

In either case, a function is continuous on its domain if it is continuous at every point in the domain. Thus a function can be continuous on either $ [a,b]$ or $ (a,b)$.

You'll find topological properties with indication of whether they are preserved by (various kinds of) continuous maps or not (such as open maps, closed maps, quotient maps, perfect maps, etc.). For …

Some people like discrete mathematics more than continuous mathematics, and others have a mindset suited more towards continuous mathematics - people just have different taste and interests. On the …

Are there any examples of functions that are continuous, yet not differentiable? The other way around seems a bit simpler -- a differentiable function is obviously always going to be continuous.