The-Organic-Chemistry-Tutor
The video covers various techniques to evaluate limits, including direct substitution, factoring, and using the common denominator and conjugate methods for complex fractions and radicals. The concept of one-sided limits is introduced, along with vertical asymptotes and jump discontinuities. The distinction between removable and non-removable discontinuities is also explained. The instructor provides multiple examples and demonstrates the graphical method of finding the limit.
In this section, the video introduces viewers to the concept of limits and how to evaluate them analytically and graphically with examples. One technique is to use direct substitution by plugging a number close to the limit value but not exactly the same, and if that leads to an undefined value, one can factor the expression to simplify the limit. The video also shows how to use the formula for a difference of cubes to factor a complex expression.
In this section, the video introduces how to evaluate limits with different types of fractions. For complex fractions, it is recommended to multiply the top and bottom by the common denominator of the two fractions, factor any similarities between the denominators, and then simplify the expression. For square roots, the conjugate should be used to eliminate the root term before canceling out any denominators. The process is demonstrated through several examples of evaluating limits as x approaches a certain value.
In this section, the concept of finding limits of functions with complex fractions and radicals is discussed. To find the limit, the common denominator method is used, where the numerator and denominator are multiplied by the same factor so that the common denominator is obtained. The conjugate is also multiplied to deal with radicals in the numerator. The graphical method is also demonstrated where finding the limit involves looking for the y value of a given point from the left and right sides of the curve.
In this section, the instructor explains the concept of one-sided limits, which are used when approaching a function from either the left or right side. If the left-sided limit and the right-sided limit are not the same, then the limit does not exist. The instructor provides examples of how to find the limits and function values when approaching certain points on a graph. The concept of vertical asymptotes and jump discontinuities is also introduced, and it is explained that when a function has a zero in the denominator, there is a vertical asymptote and the function is undefined at that point.
In this section, the concept of removable and non-removable discontinuities in calculus is discussed, with examples given. A hole in a function is considered a removable discontinuity, while a jump discontinuity and an infinite discontinuity are both examples of non-removable discontinuities.
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