How To Solve Limit Of A Function || Factorization method
In this calculus video tutorial, we will be discussing 👇
LIMIT OF A FUNCTION
In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value. Limits are essential to calculus (and mathematical analysis in general) and are used to define continuity, derivatives, and integrals. In limit it is possible that the function f(x) may not be defined for all values of x,
Limit of a function: y= x) as x approaches the point a is defined as the number L. In formulas, a limit is usually written as limn-a f(n) = L such that f(x) is close to L for all x sufficiency close to a but not necessarily equal to a. The formula also means that fix) can be made to be as close to Las desired by making x sufficiently close to a. In that case, the above equation can be read as "the limit of fof x, as x approaches a, isL".
When the left hand limit is equal to the right hand limit, we say that the limit exists. If they are not equal, we say that the limit does not exist.
When indeterminate is encountered and then result to direct
substitution, the following evaluation processes are applied:
simplification method, rationalization method, division of numerator
and denominator by the highest power of the independent variable
present and L'Hopital's rule (differentiation method))
Limit at infinity: For polynomial functions, its limit at infinity is given by the limit of the dominating term. For rational functions the limit at infinity is gotten by dividing the numerator and the denominator by the highest power of the independent variable present.
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