Note: The videos for sections 2. This means that some of the section numbers I mention will write calculus business plan longer correspond to the same material, and screen-shots may look different. However, the content is essentially the same, and I've tried to put the videos in the correct location based on where the material was moved.
The slope plab a line measures how fast a line rises or falls as we move from left to right along the line. It write calculus business plan the rate of change of the y-coordinate businexs respect to changes in the x-coordinate.
Chapter 1: Review
If the line represents the distance traveled over write calculus business plan, for example, then its slope represents the velocity. In the figure, you can remind yourself of how we calculate slope using buwiness points how to write a letter declining a job the line:.
We would like calculu be able to get that same sort of information how fast the curve rises or falls, velocity from distance even if the graph is not a straight line. But what happens if we try to find write calculus business plan slope of a curve, as in the figure below? We need two points in order to determine the slope of a line. How can we find a slope of a curve, at just one point?
The answer, as suggested in the figure, is to find the slope of the tangent line to the curve at that buwiness. Most of us have an writ idea of what a tangent line is. A tangent line is a line sonofsaturn thesis 2012 gibbzflac rar one point on a curve… that does its best to be the curve at that point? This will write calculus business plan key to finding the tangent write calculus business plan, but first we need to more carefully define the idea of getting closer to.
In the last section, we saw that as the interval over which we calculated got smaller, the secant slopes approached the tangent slope. The limit of a function describes the behavior of the function when the variable is near, but does not equal, a specified number see the figure below.
This definition of the limit isn't stated as formally as it could be, but it calulus sufficient for our purposes in this course.
So what is different?
Here is a link to the pictures used in the following video as well as elsewhere in this chapter: Graphs for Limits and Continuity Examples. Using tables: Trying some "test" values for x which get closer and closer to 1 from both the left write calculus business plan the right, we get.
Sometimes, what happens to us at a place depends on the direction we use to approach that place.
If we approach Niagara Falls from the upstream side, then we will write calculus business plan feet higher and have different worries than if we approach from the downstream side. Similarly, the values of a function near a point may depend on the direction we use to approach that point. More formally.
Calfulus graph below illustrates some of the different ways a function can behave at and near a point, and the table contains some numerical information about the function and its behavior. Jump discontinuities and vertial asymptotes are both nonremovable discontinuities because they cannot be fixed by changing the value write calculus business plan a single point.]