the limit [as x-->5] of the function f(x)=2x is 5 the limit [as x-->infinity] of the function f(x) = 2x is infinity
the limit [as x-->infinity] of the function f(x) = 1/x is 0
the limit [as x-->infinity] of the function f(x) = -x is -infinity
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Calculus involves the exploration of limits in mathematics. For example, if you consider a polygon and keep adding a side to it, eventually it will begin to look like a circle but it will never truly be a circle. This is an example of a limit.
Calculus is about applying the idea of limits to functions in various ways. For example, the limit of the slope of a curve as the length of the curve approaches zero, or the limit of the area of rectangle as its length goes to zero. Limits are also used in the study of infinite series as in the limit of a function of xas x approaches infinity.
Calculus is the branch of mathematics that studies continuously changing quantities. The calculus is characterized by the use of infinite processes, involving passage to a limit, that is, the notion of tending toward, or approaching, an ultimate value.
The term "limit" in calculus describes what is occurring as a line approaches a specific point from either the left or right hand side. Some limits approach infinity while some approach specific points depending on the function given. If the function is a piece-wise function, the limit may not reach a specific value depending on the function given. For a more in-depth definition here is a good link to use: * http://www.math.hmc.edu/calculus/tutorials/limits/
You can find LOTS of problems, often with solution, by a simple Google search, for example, for "calculus problems". Here is the first hit I got:https://www.math.ucdavis.edu/~kouba/ProblemsList.html