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Are derivative and the slope same? [closed]
I have a doubt. Please correct me if I’m mistaken. Derivative is considered as rate of change = slope isn’t it? If the derivative of $x^2$ is $2x$, that m...
Apr 20, 2026
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How to compare logarithms $\log_4 5$ and $\log_5 6$?
I need to compare $\log_4 5$ and $\log_5 6$. I can estimate both numbers like $1.16$ and $1.11$. Then I took smallest fraction $\frac{8}{7}$ which is grea...
Apr 20, 2026
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What is a bijective linear mapping called?
Friedberg - Linear Algebra p.102 This book states that "a bijective linear map from a vector space to another vector space is called an isomorphism". As f...
Apr 20, 2026
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What is an Integral Domain?
Okay, so almost 3 months into my abstract algebra, we just started rings. I have a few questions. A "trivial ring" is a ring with only one element. So $R=...
Apr 20, 2026
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Linear maps and Linear independence
If we have a set of linearly independent vectors, can they be mapped to a set of linearly dependent vectors? and vice versa. for example, Given T : V → W ...
Apr 20, 2026
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Find the volume of the solid formed by rotating completely about x-axis the area enclosed by a curve
Question: Find the volume of the solid formed by rotating completely about $x$-axis the area enclosed by a curve. My answer: I drew the curve and the area...
Apr 20, 2026
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Is the slope of a vertical line infinity or undefined?
By slope I mean derivative. Is something being infinity the same thing as being undefined? Is the slope of a vertical line negative infinity or positive i...
Apr 20, 2026
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Why do I get a saddle point and not a maximum?
We have the function $f(x,y)=36xy$ and we want to maximize it subject to $3x+6y=m$. Using the Lagrange method I found that a critical point is $\left (\fr...
Apr 20, 2026
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Infinite lists in Lambda calculus....
I have been learning Haskell for a number of months now and am now trying to understand the underpinning $\lambda$-calculus, but I have run into a bit of ...
Apr 20, 2026
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Value of Logarithm of negative number
Why the logarithmic value of negative number can't be define? Is there any special reason?
Apr 20, 2026
