An integrable function, defined on a closed interval [a. b], has an indefinite integral defined by (Mendoza, 2017):. This indefinite integral is continuous and differentiable almost everywhere. References Dettma
What is a continuous function? Different types (left, right, uniformly) in simple terms, with examples. Check continuity in easy steps.
How to check if function is continuous and differentiable? Show that the function, f(x) = \left\{\begin{matrix} (x^2 + 1), & if & x \leq -1\-2x, & if & x > -1 \end{matrix}\right. is continuous and differentiable at the value x = -1. ...
The first way of calculating the derivative of a function is by simply calculating the limit. If it exists, then you have the derivative, or else you know the function is not differentiable. Example As a function, we takef(x) = x2. (f(x+h)-f(x))/h = ((x+h)2- x2)/h = ...
What is the damping factor of the function f(x) = e^{2x} \sin x ? What are the steps in verifying that -ln|secx+tanx| = ln|secx-tanx| How to make a tessellation How to prove a manifold is differentiable? How to show that a set is convex?
We see that x is irrational iff x isn't in the range of the embedding function, i.e, x is a real number that doesn't correspond to any rational number. We check that it agrees with our intuition what "being irrational" means and go on....
We use essential cookies to make sure the site can function. We also use optional cookies for advertising, personalisation of content, usage analysis, and social media. By accepting optional cookies, you consent to the processing of your personal data - including transfers to third parties. Some...
Let g(x) and h(y) be differentiable functions, and let f(x, y) = h(y)i+ g(x)j. Can f have a potential F(x, y)? If so, find it. You may assume that F would be smooth. (Hint: Consider the mixed partial derivatives of F.) How to answer this question? Wh...
to go that deep and trust the Mathlib's implementation of number systems and conversions between them. We see that x is irrational iff x isn't in the range of the embedding function, i.e, x is a real number that doesn't correspond to any rational number. We check that it agrees ...
are commonly expressed asuniversal conditionalsof the form ‘∀x, ifA(x)thenB(x)’. Often, these are written simply ‘ifA(x)thenB(x)’ with the quantifier implicit (Schumacher,2001), as in ‘if∑n=1∞anconverges, then(an)→0’ or ‘iff:R→Ris differentiable ata, thenfis continuous...