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 Oct 22 awarded Explainer Oct 22 answered Finding a number with certain properties Oct 22 revised Finding a number with certain properties Correted spelling + condensed Oct 22 suggested approved edit on Finding a number with certain properties Oct 22 revised Calculating dimension of a vector space Fixed confusion between vector spaces and matricies. Oct 22 suggested approved edit on Calculating dimension of a vector space Oct 22 comment How to prove that a divergent limit of a function multiplied by a convergent limit of a function is divergent Remember that $\infty$ is not a number, so you can not attempt to set $L=\infty$ in the definition of a limit. Rather, you must show that there is no limit for the function by proving the negative of the definition. Oct 22 comment Epsilon-n proof confusion @StatGod I fail to see how this is a "better" $k$. It's merely a trick to make your work easier in finding a $k$ that fits the inequality. Correct me if I'm somehow wrong here, but the poster explicitly and algebraically solved for the minimum $k$ and therefore, in my eyes, an ideal one to use. Oct 21 revised Find $\frac{dy}{dx}$ equal to zero in terms of x and y Remove unneccesary character, fix typesetting Oct 21 suggested approved edit on Find $\frac{dy}{dx}$ equal to zero in terms of x and y Oct 21 revised How can I show that $\left(\frac{2}{3}\right)^n$ goes to 0 exponentially fast as n goes to infinity? typesetting Oct 21 suggested approved edit on How can I show that $\left(\frac{2}{3}\right)^n$ goes to 0 exponentially fast as n goes to infinity? Oct 21 comment How large need n to be to ensure that Taylor polynomial around x=0 gives a value of sin(pi) which has an error of less than 0.001? Your method is correct for finding the minimum value of $n$, however note that you want to have the term less than $\frac{1}{1000}$, so you should have an inequality. These inequalities can not always be solved algebraically, as in this example, so trial-and-error is an appropriate method to use. Oct 21 revised How large need n to be to ensure that Taylor polynomial around x=0 gives a value of sin(pi) which has an error of less than 0.001? Typesetting + spelling Oct 21 suggested approved edit on How large need n to be to ensure that Taylor polynomial around x=0 gives a value of sin(pi) which has an error of less than 0.001? Oct 21 comment Finding equation from log log graph That's exactly what you can do. Bear in mind that the equation of a line in the log-log plane is not $y=m\cdot x + b$, but rather $\log y = m \cdot \log x + b$. Work from that and you can solve for $y$ as a function of $x$ Sep 8 awarded Yearling Dec 20 awarded Constituent Dec 8 comment How can we find another path I don't know what the actual question is asking you to do. But, it is sufficient to determine the partial derivatives of this function. You will see that they do not exist at (0,0), therefore the function can not be differentiable at that point. Dec 8 comment How can we find another path What have you done so far?