University:
Rice University
Course:
MATH 212 | Multivariable Calculus
Academic year:

2022
Views:

401

Pages:

1
Author:

FredCy

Finding Limits Analytically. Example Problem 1 We can find the limit of an algebraic expression in several ways. One way is to use simple substitution, but that doesn't work for indeterminate forms; evaluating numerator and denominator with negative 4 will yield 0/0. To clear up the 0/0, we need to factor. The top factors of 4x – 10 are 4x + 2 and 4x – 2. The denominator factors of 4x – 10 are 4x + 2 and 4x. Both the numerator and denominator have a factor of 4x + 2, so if you add these two equations together, you will get a true statement. Thus, as x approaches negative 4, we have the derivative of x minus 10 divided by x plus 2. Because the numerator and denominator both equal 1, we eliminate the problem of division by 0. We have taken the expression 0/0 out of the limit. Therefore, we are left with only the numerator and denominator as fractions to simplify. To evaluate the limit again, plug in negative 4. We will evaluate it in the same way we evaluated it earlier by dividing the numerator and denominator by 2. By doing so, we get −14/2, which is −7. The limit is −7.