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Evaluating the limit of $\ln(2x)/\ln(x)$ as $x\to\infty$
I'm trying to evaluate the following limit: $\displaystyle\lim_{x \to \infty} \displaystyle\frac{\ln(2x)}{\ln(x)}$ Using L'Hospital's rule,...
Apr 21, 2026
Archive: News
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How come the time complexity of Binary Search is log n
I am watching this professor's video on Binary Search but when he reached here, I am a bit lost. How come he came up the time coomplexity is log in j...
Apr 21, 2026
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Calculate surface area of a F using the surface integral
Task Given: $$F := \{(x,y,z) \in \mathbb{R}^3 \mid (x,y) \in W,z=f(x,y)\}$$ Calculate the surface area using the surface integral: $i) \; f(x,y) := x+y \;...
Apr 21, 2026
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I need help understanding the Nested Interval Property
In my textbook we have the theorem that For each $n \in N$, assume we are given a closed interval $$I_n = [a_n, b_n] = \{x \in R : a_n ≤ x ≤ b_n\}.$$ Assu...
Apr 21, 2026
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What does it mean if the discriminant of a discriminant is negative?
What does it mean if the discriminant of a discriminant is negative? For example $x^2+(m+1)x+(m-2)=0$ $b^2-4ac=m^2-2m+9$ and the discriminant of that $=-3...
Apr 21, 2026
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Fano's inequality explained intuitively?
I am now reading through a book to understand Fano's inequality, but I remember my professor explaining it in a certain way that made it seem so logi...
Apr 21, 2026
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Why derivative is a slope?
The change of $Y$ per $X$ is slope. And some say the change of slope per $X$ is derivative. So it is like slope of a slope! But slopes are always numbers ...
Apr 21, 2026
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How to express sin(y) in terms of cos(y)?
The first question asked to express a equivalent expression in of $\cos(x+y)$ for which I got right. However its the second part of the question that I do...
Apr 21, 2026
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Beta distribution density function - integration problem
I want to calculate $EX$ of beta distribution given by certain formula (if necessary i will post it) i am stuck with an integral of this sort: $$\int_0^1\...
Apr 21, 2026
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To Prove $x'Ax=\mathrm{tr}(xAx')=\mathrm{tr}(Axx')=\mathrm{tr}(xx'A)$
To prove, $x'Ax=\mathrm{tr}(xAx')=\mathrm{tr}(Axx')=\mathrm{tr}(xx'A)$ where $A$ is a square matrix. $x'$ is the transpose of $x...
Apr 21, 2026
