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 Sep21 comment lim calculus problem with infinity Also, the nth-root of n goes to $1$. If you don't believe me, take the logarithm of the expression. Sep21 comment lim calculus problem with infinity The fraction goes to $1$ but the exponent goes to $\infty$; this doesn't go to $1$ but rather is an indeterminate case, as evidenced by the well known fact that $(1+\frac1{n})^n \to e$. Sep20 answered lim calculus problem with infinity Sep20 revised lim calculus problem with infinity added 25 characters in body Sep18 comment Does infinite time = time with no end = never? The short answer is that if it takes an infinite amount of time to reach point B, then the object never reaches it. Of course, in the real world, no matter how precise your measurement is, there will be some time after which the object is closer to B than your instrument can distinguish. Sep17 awarded Popular Question Sep17 reviewed Reject Property of $W_0^{1,p}(\Omega)$ Sep16 answered Solving one-sided limits analytically Sep10 comment Infinite amount of additions, finite sum? @ZoltánSchmidt: While I found your question interesting, I think at some point you just need to accept that adding an infinite amount of terms can result in a finite result, and the intuition will come later. Someone on this site once quoted something along the lines of "In math, we don't understand things; we just get used to them". Try to work out the $\sum \frac1{2^n}$ example. It's easy to do and it will give you some insight as to why the total sum is $2$ and not $\infty$. Sep10 comment Is it true that $\sum \limits_{i=1}^{\infty} f(i) = \lim_{n \to \infty} \sum \limits_{i=1}^{n} f(i)$? By the way, it doesn't make sense to ask if this holds for all $n$, since $n$ isn't a free variable. Sep9 revised Why can't we substitute in limits for other limits? added 2 characters in body Sep8 comment $f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$ $f$ can't be one-to-one, since for example $f(0) = f(\frac14)$. Sep7 answered Problem with differentiation as a concept. Sep7 comment Problem with differentiation as a concept. Small correction: The definition is either $\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$ or $\lim_{x \to x_0} \frac{f(x)-f(x_0)}{x-x_0}$. Sep4 comment Integration of function The binomial theorem proper only works when the power is a positive integer. You could get a series expansion, but otherwise I doubt this has a closed form. If it was a definite integral, you may be able to relate to the beta function using the substitution $u=\frac{a}{x}$. Sep4 comment Integration of function Please make sure I did the LaTeX right. Is it $1+\frac{a}{x}$ or $\frac{1+a}{x}$? Sep4 revised Integration of function latex Sep3 answered Reasoning Behind Holes in Rational Functions Sep2 comment Easy way to find the streamlines If you're not supposed to do it rigorously, then sketching $\mathbf{F}$ at a few select points can give you an idea. Sep2 comment What's the Period of This Function? Try graphing it, for particular values of $k$.