query: How is an infinitesimal $dx$ different from $\Delta x\,$?
positive_passages.docid: 3360
positive_passages.text: Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio?
negative_passages.docid: 71885
negative_passages.text: Derivatives of $ \frac{1}{r} $ and Dirac delta function
negative_passages.docid: 83790
negative_passages.text: Why doesn't $d(x_n,x_{n+1})\rightarrow 0$ as $n\rightarrow\infty$ imply ${x_n}$ is Cauchy?
negative_passages.docid: 127964
negative_passages.text: Confused about the possibility of different differentiable structures.
negative_passages.docid: 73099
negative_passages.text: Why is $d(x^2)= 2xdx$?
negative_passages.docid: 13018
negative_passages.text: Why is $1^{\infty}$ considered to be an indeterminate form
negative_passages.docid: 69507
negative_passages.text: What is the meaning of infinitesimal?
negative_passages.docid: 151493
negative_passages.text: Using $\epsilon$-$\delta$ to show a property of a function
negative_passages.docid: 109570
negative_passages.text: How to show that the set of points of continuity is a $G_{\delta}$
negative_passages.docid: 68863
negative_passages.text: Delta function potential in an infinite square well
negative_passages.docid: 142821
negative_passages.text: Why?$\int_0^1\int_{u(t)}^{u(t)+w(t)} f(t,v(t)) dv dt = \int_0^1 f(t,u(t)+\theta w(t))w(t) dt; ~~\theta\in[0,1] $
negative_passages.docid: 98913
negative_passages.text: Sign in $\Delta U= -\int\vec{F}\cdot d\vec{l}$
negative_passages.docid: 146699
negative_passages.text: Dirac Delta Function of a Function
negative_passages.docid: 8408
negative_passages.text: What is $dx$ in integration?
negative_passages.docid: 158610
negative_passages.text: Why is the differentiation of $e^x$ is $e^x$?
negative_passages.docid: 25646
negative_passages.text: What is the result of $\infty - \infty$?
negative_passages.docid: 135092
negative_passages.text: How exactly can't $\delta$ depend on $x$ in the definition of uniform continuity?