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

Info iconThis 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?
Background image of page 1

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

View Full DocumentRight 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 :
Background 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:
Background image of page 3

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

View Full DocumentRight 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 ) can be made as close to the number L as we please by taking
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/21/2012 for the course MATH 1314 taught by Professor Marks during the Fall '08 term at University of Houston.

Page1 / 11

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online