In a
previous post, we talked about using substitution to find the limit of a function. Sometimes substitution does not immediately work, like when the limit is one of the indeterminate forms. In this case, we must algebraically manipulate the function first. We will focus on factoring the function in order to use substitution.
Here we will work out the first problem step by step (
click here):
1. Try Substitution:
When we substitute 2 in for x, we get 0/0, an indeterminate. Therefore, we must manipulate the fraction.
2. Factor both the numerator and denominator:
Once factored, the numerator and the denominator showed that they have a common factor, (x-2). This factor was then cancelled out, leaving a simplified fraction.
3. Substitute
Here is another example using factoring (
click here):
Last example … (
click here):
I did not find factoring to be too challenging. The only obstacle I came across when dealing with limits was remembering that factoring is an option. Don’t forget that there are multiple ways to solve the limit.
Until Next time,
Leah
Hey Guys! I’m Leah Weil. I am interning with Symbolab for the summer and will be writing some of the upcoming blogs. I will tell you a little bit about myself. I am from Cincinnati, OH, but I currently live in Columbus, OH. I am about to start my 3rd year at the Ohio State University studying math, with a minor in Hebrew. I have an older sister who lives in New York and at home I have two dogs. Please comment the posts if you have any questions or comments. Thanks!
