Use series to evaluate limit
limit as x approach infinity of $3(x^2)(e^{-2/x^2}-1)$. I don't know what series to use.
18 Apr 2026 1 READS
Archive: General
How to find whether point is maxima/minima/saddle point for this case?
I read that we have a formula to check signs of $f_{xx}*f_{yy}-(f_{xy})^2$ and $f_{xx}$ And then we conclude whether the point is a maxima minima or saddl...
18 Apr 2026 1 READS
How to check the differentiability of this function.
Question: Let $\text{f(x) = max{1-x, 1+x, 2}}$. Prove that $f(x)$ is continuous at all points but not differentiable at $x = 1$ and $x = -1$. Doubt: I che...
18 Apr 2026 1 READS
Finding depressed equation without a divisor
I've been given $$4x^3 -2x^2 + x - 3 = 0$$ and I want to convert it into a depressed equation. A depressed equation is an equation that results from ...
18 Apr 2026 1 READS
Number of ways to choose 4 among 10 if repetition is allowed
Q: In how many ways can you choose 4 things among 10 if the order does not matter and you can choose the same item several times? I am trying to understan...
18 Apr 2026 1 READS
![Quadrilateral $ABCD$ with $AB=AD$, $\angle BAD=60^\circ$, $\angle BCD=120^\circ$. Prove $BC+DC=AC$ [closed]](https://edu.smbbmcl.edu.pk/uploads/quadrilateral-abcd-with-ab-ad-angle-bad-60-circ-angle-bcd-120-circ-prove-bc-dc-ac-closed_720.jpg)
Quadrilateral $ABCD$ with $AB=AD$, $\angle BAD=60^\circ$, $\angle BCD=120^\circ$. Prove $BC+DC=AC$ [closed]
In a given quadrilateral $ABCD$, we have $$AB = AD, \angle BAD = 60^\circ, \angle BCD = 120^\circ$$ Prove that $$ BC + DC = AC$$ I know the quadrilateral ...
18 Apr 2026 1 READS
Area under an exponentail curve without integration
Given is the graph of an exponential function $f\left(x\right) = \mathrm{exp}\left(-x\right)$. I need to find the area under it in an interval $A$. Is the...
18 Apr 2026 1 READS
Proof of 'sandwich theorem' for sequences
Please bear with me here and please try to read it all and spot any mistakes or errors as I'm trying to prove this result but I'm unsure of whet...
18 Apr 2026 1 READS
Angle of rotation by pure unit quaternions(fundamental unit quaternions)
From the versor definition here, i understand that versor is a unit quaternion and also a pure quaternion with its scalar part zero. So, versor is a pure ...
18 Apr 2026 1 READS
What are the origin and reason of the name matrix?
I wondered why the term matrix had been chosen as the name for what otherwise looks like a table of numbers. Is there any originator and (speculative) rea...
18 Apr 2026 1 READS
