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How to find singular points of a function without knowing the graph?
Problem: Let $f(x) = (x-1)^{2/3} - (x+1)^{2/3}$. Locate and classify all local extreme values of this function. Determine whether any of these extreme val...
Apr 21, 2026
Archive: News
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Meaning of more likely or less likely in probability
Suppose, I'm performing a certain experiment with many outcomes corresponding to $4$ events - $A,B,C,D$. We have been given the following data : $$p(...
Apr 21, 2026
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Derivative of inverse trigonometric functions: $f(x)=\arcsin\left(2x\sqrt{1-x^2}\right)$
While trying to find the derivative of $$f(x)=\arcsin\left(2x\sqrt{1-x^2}\right)$$ we arrive at two different answers by substituting $x=\sin t$ or $x=\co...
Apr 20, 2026
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Can an undirected graph be disconnected?
This may be a rather trivial question but I am still trying to get the hang of all the graph theory terms. Nonetheless, I haven't found a source that...
Apr 20, 2026
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Finding a plane parallel to a line
So I've been stuck on this question. Find a plane that will have no points of intersection with the line $L1.$ $L1$ passes through the point $P(1,−2,...
Apr 20, 2026
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Why is there special notation for the tensor product? (Multilinear algebra of real vector spaces)
The following definition is from p. 306 of the 2nd edition of John Lee's Introduction to Smooth Manifolds -- note that I have seen similar definition...
Apr 20, 2026
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Find E(X) from Moment Generating Function
Let $$M(t)=\frac{5}{1-8t}$$ for $t<1/8$ be the mgf of random variable $X$. Find $E(X)$ and $Var(x)$. I am not sure how to use the mgf to find the $E(X)...
Apr 20, 2026
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Scalar-valued function definition
A scalar-valued function is defined to be a function with a single number as its output. What is the logical origins of giving this type of function the n...
Apr 20, 2026
![Evaluate the Difference quotient $[f(x) - f(a)] / (x-a) $ for the given function $f(x) = 1/x .$](https://news.conceivablytech.com/uploads/evaluate-the-difference-quotient-f-x-f-a-x-a-for-the-given-function-f-x-1-x_720.jpg)
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Evaluate the Difference quotient $[f(x) - f(a)] / (x-a) $ for the given function $f(x) = 1/x .$
$f(x) = 1/x , [f(x) - f(a)] / (x-a)$ How do I go about setting this up? If $f(x)= 1/x$ does this term only apply to $f(x)?$ What do I do with the $f(a)? $...
Apr 20, 2026
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What does it mean that a function dominates over another function?
Let $f,g$ be functions with Domain $\mathbb{R}$ and Range $\mathbb{C}$ What does it mean that $f$ dominates over $g$? Unfortunately I could not find any r...
Apr 20, 2026
