Hi, I've a doubt about the definition of curve. A smooth curve in ##\mathbb R^2## is defined by the application ##\gamma : I \rightarrow \mathbb R^2##. Consider two maps ##\gamma## and ##\gamma'## that happen to have the same image (or trace) in ##\mathbb R^2##. ...
smooth surface (redirected fromSmooth function) Also found in:Encyclopedia,Wikipedia. smooth sur·face (smūdh sŭrfăs) Proximal,buccal,andlingualareasofteeth. MedicalDictionaryfortheDentalProfessions©Farlex2012 Want to thank TFD for its existence?Tell a friend about us, add a link to this pa...
A curved line is one that is not straight and is bent. Ideally, it is smooth and continuous. In other words, a curve is defined as a group of points that resemble a straight line that falls between two neighbouring points. We know that the curvature of the straight line is zero. Hence...
Forum: Precalculus Mathematics Homework Help I A curve that does not meet rational points This is just to recall a nice fact: Any two points ##A,B\in\mathbb{R}^n\backslash\mathbb{Q}^n,\quad n>1## can be connected with a ##C^\infty##-smooth curve that does not intersect ##\...
A function f(x) is said to be a continuous function in calculus at a point x = a if the curve of the function does NOT break at the point x = a. The mathematical definition of the continuity of a function is as follows. A function f(x) is continuous at a point x = a if...
It is astationary point, and the curve or surface in its neighborhood is not entirely on any side of itstangent space. Multiple Saddle Point Surfaces A smooth surface which has one or more saddle points is called asaddle surface. The graph above would be an example of a saddle surface; ...
A curve is defined as continuous and smoothly- flowing lines that do not have any sharp turns. Learn the different types of curves in 2D and 3D geometry with examples at BYJU’S.
The two peaks mean that there are two groups in the frequency table that has the most frequency of occurrence. This also means that the data is showing two modes in the measures of central tendency. What does a unimodal graph look like? A unimodal graph will look like a smooth curve ...
Generally speaking, an arc of a circle is a smooth curved bounded by two distinct points. Alternatively, any arc is a portion of the circumference of a circle, bounded by two points, rather than the entire circle. Arc length is the distance of the arc bounded by two points. A sector ...
Forum:Calculus Q Gradients and Tangents to Level Curves Homework Statement Find the gradient of the function at the given point, then sketch the gradient together with the level curve that passes through the point. f(x,y) = y - x (2,1) Homework Equations gradient of f = (df/dx)i +...