A sequence can be thought of a list of numbers written in a definite order:
a1, a2, a3, ..., a(n+1), an, ...
The number a1 is called the first term, a2 is the second term, and in general an is the nth term.
For every positive integer n, there is a corresponding number an, and so a sequence can be defined as a function whose domain is the set of all positive integers. But, we usually write an instead of the function f(n) for the value of the function at the number n.
Notation: The sequence {a1, a2, a3, ...} is also denoted by {an}.
Some sequences can be defined by giving a formula for the nth term. For example:
an = (n)/(n +1) the sequence is {1/2, 2/3, 3/4, 4/5, ..., (n)/(n+1), ...}
this sequence can be pictured either by plotting its terms on a number line, or by plotting its graph. Since a sequence is a function whose domain is the set of positive integers, its graph consists of isolated points with coordinates (1, a1), (2, a2), (3, a3), ..., (n, an).
Try to plot the graph of this sequence, and you will see that the terms of the sequence an = n/(n+1) are approaching 1 as n becomes large. In this case 1 is the limit for this sequence, and we can write:
lim n -->∞ an = 1
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∙ 15y agoWhen a graph shows a trend that is noticeable. Such as a line or a curve in a certain shape.
price or equilibrium A curve
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A differentiable function, possibly - to distinguish it from one whose graph is a kinked curve.
An energy versus time graph shows how much energy is spent as set intervals of time. If the amount is constant, the line is a straight line. if the amount of energy changes, the line becomes a curve.
it is a line on a graph that is curved
The slope of the graph line or curve.
When a graph shows a trend that is noticeable. Such as a line or a curve in a certain shape.
price or equilibrium A curve
A fraction is a single value. At is neither a graph nor a curve.
What does a steep looks like
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rapid
Draw a graph of a given curve in the xoy plane. Now draw a vertical line so that it cuts the graph. If the vertical line cuts the graph in more than one ordinate then given graph is not a function. If it cuts the graph at a single ordinate such a graph is a function.(is called vertical line test)
This question cannot be answered in a sensible way because it is based on a misunderstanding. The dots in a line graph ARE connected. That is what a line graph is. If they are not connected then it is a scatter graph.
The curve on the graph for a filament lamp is due to the relationship between current and voltage in the lamp. As the current passing through the filament increases, the resistance also increases, leading to a non-linear relationship between current and voltage. This results in a curve on the graph instead of a straight line.
It is the gradient (slope) of the line.