Video 2
Determining limits by Inspection
there are two conditions that must be match before determining limits by inspection. First is x goes to positive or negative infinity and second the limit involves a polynomial divided by a polynomial. For example this is the problem earlier if from this case we can see that is polynomial over polynomial and x approaches infinity.
The key to determining limit by inspection is in looking at power of x in the numerator and the denominator.And remember to apply this rule you must be dividing by a polynomials and x has to be approaching infinity.
The first shortcut rule said “ if the highest power of x is greater in numerator than the denominator, then the limit is positive or negative infinity.
For the example if, . Since the highest power of x in the numerator 3 is the greater than the power of x square, the limit value is positive or negative infinity.Since all of the number is positive, and x is going to positive infinity, limit must be positive infinity.If you can’t tell if the answers is positive or negative infinity, you can subtitute in a large number for x and see if you end up with a positive or negative number.Whatever the sign you get is the sign of infinity for the limit.
The second shortcut rule set that if the highest power of x is in the denominator, then the limit inspection is zero. And the last shortcut rule can be used when highest power of x in numerator is same as highest power of x in denominator.If this is case, the limit of negative or positive infinity it just the quotient of the coefficients of the two highest powers. And the mean of coefficient is the number that the goes with a variable