How to find limits of functions
Calculation of limits of functions - the foundation of mathematical analysis, which devoted a lot of pages in the textbooks. However, sometimes it is not clear not only the definition but also the very essence of the limit. In simple terms, the limit - it is the approach of one variable, which depends on the other, to any particular single value with changes that other values. To successfully calculate enough to keep in mind a simple algorithm solutions.
Instruction how to find limits of functions
Place a limit point (aspiring to any number of "x") in the expression after the limit sign. This method is most simple and saves a lot of time, since the result is a single digit. If there are uncertainties, you should use the following paragraphs.
Remember the definition of a derivative. From this it follows that the rate of change of the function is inextricably linked to the limit. Therefore, we calculate the derivative of any limit on the rule of L'Hospital-Bernoulli: a limit of two functions is equal to the ratio of their derivatives.
Shorten each term on the senior level of the variable in the denominator. As a result of the calculation you will or infinity (if the highest power over the denominator is as much the numerator), or zero (on the contrary), or a number.
Try to expand the fraction factorization. The rule is effective for 0/0 of the form of uncertainty.
Multiply the numerator and denominator in the expression of the conjugate, especially if after «lim» has roots that give the uncertainty of the form 0/0. The result is a difference of squares without irrationality. For example, if the numerator is an expression of irrational (root 2), that is multiplied by equal to it, with the opposite sign. From the roots of the denominator will not go away, but they can find by following the claim 1.