What does it mean when a graph is smooth?

What does it mean when a graph is smooth?

A smooth curve is a curve which is a smooth function, where the word “curve” is interpreted in the analytic geometry context. In particular, a smooth curve is a continuous map from a one-dimensional space to an. -dimensional space which on its domain has continuous derivatives up to a desired order.

How do you know if a graph is smooth?

A curve defined by x=f(t),y=g(t) is smooth if f′(x) and g′(x) are continuous and not simultaneously zero.

What does it mean when a graph is smooth and continuous?

A graph for a function that’s smooth without any holes, jumps, or asymptotes is called continuous.

What does smooth curve mean in calculus?

Smooth Curve in Calculus In general, a smooth curve is a rectifiable curve created on an interval from a differentiable function. A curve is smooth if every point has a neighbourhood where the curve is the graph of a differentiable function.

Where is a curve smooth?

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For an algebraic curve of degree n, with , the curve is smooth in the real (resp. complex) projective plane if the system has no other real (resp. complex) solution than (0, 0, 0). A curve is said to be smooth if it has no singular points, in other words if it has a (unique) tangent at all points.

How do you know if a function is L smooth?

Note that we call a function L-smooth if it is continously differentiable and its gradient is Lipschitz continuous with Lipschitz constant L: ∇/(x) − ∇/(y)2 ≤ Lx − y2 ∀x, y ∈ Rn. If / is twice continuously differentiable, this is equivalent to H(x)2 ≤ L for all x ∈ Rn.

What is a smooth curve calculus?

Smooth Curve in Calculus In general, a smooth curve is a rectifiable curve created on an interval from a differentiable function. A curve is smooth if every point has a neighbourhood where the curve is the graph of a differentiable function. A curve can fail to be smooth if: It intersects itself, Has a cusp.

Which curve is a smooth freehand curve?

This is a familiar concept, and is briefly described for drawing frequency curves. In case of a time series a scatter diagram of the given observations is plotted against time on the horizontal axis and a freehand smooth curve is drawn through the plotted points.

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How do you tell if a graph is continuous or discrete?

When figuring out if a graph is continuous or discrete we see if all the points are connected. If the line is connected between the start and the end, we say the graph is continuous. If the points are not connected it is discrete. Let’s now look at some application examples of discrete and continuous things.

What is the difference between smooth and continuous?

A smooth function is infinitely differentiable. Continuous functions don’t need to possess derivatives at all. See the Weierstrass function for an example of a function which is continuous but nowhere differentiable. Continuity means the function itself has no breaks.

What is smooth math?

In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous).

What is smoothsmooth line graph?

Smooth line graph is a graph that is drawn by hand. Bit like the one shown in the picture above. Notice how the curve is smooth and not jagged.

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What is the smoothing line after the points on a graph?

Again, the smoothing line comes after our points which means it is another layer added onto our graph: Note that the geom_smooth () function adds confidence bands on the smooth as well. We can remove these by adding se=FALSE inside the geom_smooth () function: This produces the following plot:

What is the smoothsmoothness of a curve?

Smoothness is a relative concept and is problem specific. $C^{(\\infty)}$ is as smooth as smooth can be. In applications, when you say the curve is smooth it means till the derivatives you are interested in the curve has to be continuous.

What is a smooth curve in analytical geometry?

A smooth curve which is studied under Analytical Geometry is nothing but a continuous curve that has derivatives upto any required order. For example, all polynomials, e^x, sin x, cos x etc., have smooth curves. However, for example, the Step function [x] jumps from -1 to 1 when x takes the value 0.