Example Problem. Finding Limits Graphically

University
Rice University
Course
Preparing for the AP Calculus AB Exam
Pages

1

Academic year

2023
Author

Fantasticsa
Views

82

p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:16px;font-family:ArialMT;color:#000000;} .ft02{font-size:16px;line-height:21px;font-family:ArialMT;color:#000000;} Finding Limits Graphically. Example Problem The function f(x) approaches the y value of three as x approaches the x-value of three.If we examine the function f(x) from the left-hand side and trace it toward the x value inquestion, we see that it appears to approach 0, but let's do the other side as well. We're examining the limit of , and we see that as the y value approaches 0, the numericalvalue of x gets closer and closer to 2. Therefore, we can say that the limit of as xapproaches 2 is 2. If x approaches negative 4, the value of this function f of x approaches −4.As the x-value gets closer to negative 4, the y-value approaches 4. As the x-valueapproaches zero from the other side, the y-value again approaches 4. Another interesting property of this function (red color) is that as x approaches negative 6,the value of f(x) approaches infinity. As we trace the function, the y value seems to begetting larger and larger without bound (positive infinity). How about at 0. Limit as x approaches 0 of this function f of x. Limit as x approaches 0 fromthe negative limit as x approaches 0 from the positive. This 0 to the negative means the lefthand side. 0 to the positive means the right hand side. In other words, instead of looking atboth arrows together, you can just look at one.So the limit as x approaches negative 6 on the left would be positive infinity, and the limitfrom the right would be positive infinity.As we approach the left endpoint, we are approaching a vertical asymptote with a y-valueof 4.As we approach 0 from the right-hand side, tracing back towards the right, we seem to beapproaching a y value of -3.Limit is one single y value.We can see that as x approaches infinity, the function f (x) approaches a horizontalasymptote with a limiting value of 3.