Essay Writing-Sample Sites - Finding Good College Essay Writing Service

Essay Writing-Sample Sites - Finding Good College Essay Writing ServiceYou need essay writing samples for your child's college applications. Most of the people say that there are hundreds of websites out there that claim to offer you with essay writing samples but actually they are not giving you any real help at all. In this article, I will list down some of the websites that are good enough to provide you with good help.WebsterGram is one of the best essay writing samples sites that are available on the internet. The site not only provides you with essay writing samples but also provides you with essay writing tips and guidelines as well.There are many sites that offer you with essay writing samples that are available in different grades. While most of the writers out there can write high school essays, they can't write any college essays.So if you want to write a college essay for your high school year, then the only solution is to go for a professional writing service. The servic es provided by a writing service may not be very expensive at all. The reason why most of the students don't use this service is because they do not have time to spend on it.The main reason for this is that most of the students are going through so much pressure from their parents. As a result, they are not able to spend more time on writing their essays. Also, writing an essay requires one to spend time on brainstorming the topics and ideas.So if you are going to write a high school or a middle school grade essay, it is advisable that you use a professional essay writing service. These services are highly effective and most of the students are going to prefer them over any other service provider. So if you are looking for essay writing samples for your school year, I suggest that you go for these services. This kind of essay writing samples are generally provided for the students in their formative years of high school. The reasons for this are that in such a scenario, a student is not able to write a good college grade essay due to lack of time. It is also not advisable for a student to write his or her college essays on their own.So next time you are looking for essay writing samples for your high school year, I strongly suggest that you go for these sites. Besides this, I am also suggesting that you get yourself a good essay writing service as a matter of fact because if you are going to take a great deal of effort in writing your college essays, then I think you should also have a resource of reference that can guide you with all the wrong moves.

AP Calculus 10-Step Guide to Curve Sketching

What can calculus tell us about curve sketching? It turns out, quite a lot! In this article, youll see a list of the 10 key characteristics that describe a graph. While you may not be tested on your artistic ability to sketch a curve on the AP Calculus exams, you will be expected to determine these specific features of graphs. Guide to Curve Sketching The ten steps of curve sketching each require a specific tool. But some of the steps are closely related. In the list below, youll see some steps grouped if they are based on similar methods. Algebra and pre-calculus Domain and Range y-Intercept x-Intercept(s) Symmetry Limits Vertical Asymptote(s) Horizontal and/or Oblique Asymptote(s) First Derivative Increase/Decrease Relative Extrema Second Derivative Concavity Inflection Points Some books outline these steps differently, sometimes combining items together. So its not uncommon to see The Eight Steps for Curve Sketching, etc. Lets briefly review what each term means. More details can be found at AP Calculus Exam Review: Analysis of Graphs, for example. Step 1. Determine the Domain and Range The domain of a function f(x) is the set of all input values (x-values) for the function. The range of a function f(x) is the set of all output values (y-values) for the function. Methods for finding the domain and range vary from problem to problem. Here is a good review. Step 2. Find the y-Intercept The y-intercept of a function f(x) is the point where the graph crosses the y-axis. This is easy to find. Simply plug in 0. The y-intercept is: (0, f(0)). Step 3. Find the x-Intercept(s) An x-intercept of a function f(x) is any point where the graph crosses the x-axis. To find the x-intercepts, solve f(x) = 0. Step 4. Look for Symmetry A graph can display various kinds of symmetry. Three main symmetries are especially important: even, odd, and periodic symmetry. Even symmetry. A function is even if its graph is symmetric by reflection over the y-axis. Odd symmetry. A function is odd if its graph is symmetric by 180 degree rotation around the origin. Periodicity. A function is periodic if an only if its values repeat regularly. That is, if there is a value p 0 such that f(x + p) = f(x) for all x in its domain. The algebraic test for even/odd is to plug in (-x) into the function. If f(-x) = f(x), then f is even. If f(-x) = f(x), then f is odd. On the AP Calculus exams, periodicity occurs only in trigonometric functions. Step 5. Find any Vertical Asymptote(s) A vertical asymptote for a function is a vertical line x = k showing where the function becomes unbounded. For details, check out How do you find the Vertical Asymptotes of a Function?. Step 6. Find Horizontal and/or Oblique Asymptote(s) A horizontal asymptote for a function is a horizontal line that the graph of the function approaches as x approaches or -. An oblique asymptote for a function is a slanted line that the function approaches as x approaches or -. Both horizontal and oblique asymptotes measure the end behavior of a function. For details, see How do you find the Horizontal Asymptotes of a Function? and How do you find the Oblique Asymptotes of a Function?. Step 7. Determine the Intervals of Increase and Decrease A function is increasing on an interval if the graph rises as you trace it from left to right. A function is decreasing on an interval if the graph falls as you trace it from left to right. The first derivative measures increase/decrease in the following way: If f(x) 0 on an interval, then f is increasing on that interval. If f(x) 0 on an interval, then f is decreasing on that interval. Step 8. Locate the Relative Extrema The term relative extrema refers to both relative minimum and relative maximum points on a graph. A graph has a relative maximum at x = c if f(c) f(x) for all x in a small enough neighborhood of c. A graph has a relative minimum at x = c if f(c) f(x) for all x in a small enough neighborhood of c. The relative maxima (plural of maximum) and minima (plural of minimum) are the peaks and valleys of the graph. There can be many relative maxima and minima in any given graph. Relative extrema occur at points where f(x) = 0 or f(x) does not exist. Use the First Derivative Test to classify them. This graph increases, reaching a relative maximum, then decreases into the relative minimum, and finally increases afterwards. Step 9. Determine the Intervals of Concavity Concavity is a measure of how curved the graph of the function is at various points. For example, a linear function has zero concavity at all points, because a line simply does not curve. A graph is concave up on an interval if the tangent line falls below the curve at each point in the interval. In other words, the graph curves upward, away from its tangent lines. A graph is concave down on an interval if the tangent line falls above the curve at each point in the interval. In other words, the graph curves downward, away from its tangent lines. Heres one way to remember the definitions: Concave up looks like a cup, and concave down looks like a frown. The second derivative measures concavity: If f(x) 0 on an interval, then f is concave up on that interval. If f(x) 0 on an interval, then f is concave down on that interval. Step 10. Locate the Inflection Points Any point at which concavity changes (from up to down or down to up) is called a point of inflection. Any point where f(x) = 0 or f(x) does not exist is a possible point of inflection. Look for changes in concavity to determine if these are actual points of inflection. This graph shows a change in concavity, from concave down to concave up. The inflection point is where the transition occurs. Final Thoughts This short article only outlines the steps for accurate curve sketching. Now its up to you to familiarize yourself with the various methods and tools that will help you to analyze the graph of any function.