{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lesson 1-b - Math 1314 Lesson 1 Limits What is calculus The...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 1314 Lesson 1 Limits What is calculus? The body of mathematics that we call calculus resulted from the investigation of two basic questions by mathematicians in the 18 th century. 1. How can we find the line tangent to a curve at a given point on the curve? 2. How can we find the area of a region bounded by an arbitrary curve?
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
The investigation of each of these questions relies on the process of finding a limit , so we’ll start by informally defining a limit and follow that by learning techniques for finding limits. Limits Finding a limit amounts to answering the following question: What is happening to the y - value of a function as the x -value approaches a specific target number? If the y -value is approaching a specific number, then we can state the limit of the function as x gets close to the target number. Example 1 :
Image of page 2
It does not matter whether or not the x value every reaches the target number. It might, or it might not! Example 2 : When can a limit fail to exist? We will look at two cases where a limit fails to exist (note: there are more, but some are beyond the scope of this course). Case 1 : The y value approaches one number from numbers smaller than the target number and it approaches a second number from numbers larger than the target number:
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Case 2 : At the target number for the x -value, the graph of the function has a vertical asymptote. For either of these two cases, we would say that the limit as x approaches the target number “does not exist.” Definition : We say that a function f has limit L as x approaches the target number a , written L x f a x = ) ( lim if the value f ( x
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern