Free essays on Calculus are written pieces of work that discuss different topics and concepts related to Calculus. These essays range from introductory topics such as derivatives and integrals to more complex topics such as differential equations and calculus of multiple variables. The essays are often written by experts in the field or by students who have an interest in sharing their knowledge with others. The essays are available online and can be accessed for free, allowing anyone to gain an understanding of Calculus without the constraints of cost.
Level Curves and Partial Derivatives. Contour Plots and Level Curves
Level curves and partial derivatives. Contour plots and level curves The contour plot is another way to look at functions of two variables. It gives a slightly different view of the surface than the standard plot, and it's useful for visualizing regions where the function has extreme values. A contour plot is a way of representing the function of two variables by using a map. The same way that when you walk around, you have actual geographical maps that fit…...
Calculus
Simplifying Equations for Analysis
Rearranging the formula The equations we have to solve are as follows: <=>{sum_(i=1)^n (X_i^2 a+X_i b-X_iY_i)=0 {sum_(i=1)^n (X_i a+b-y_1)=0 So the first equation can be simplified by looking at the coefficients of a and b. You'll see that there are actually linear equations in a and b, so there's a lot of clutter with all these x's and y's all over the place. Let's simplify the formula by dividing out the factors of two. We can eliminate a and b…...
Calculus
L’Hopital’s Rule. Example Problem
L'Hopital's Rule. Example Problem lim_(x->0) (cos(3x)-e^4x)/(x^2 -3x) lim_(x->0) (-3sin(3x)-4e^4x)/(2x-3)=-4/-3 =4/3 Let us consider the following example of L'Hopital's rule. If you evaluate the cosine of 0, you get 1. The exponential of 0 is 1, divided by 0 minus 0 - we get 0/0. Factoring probably won't work, since there are no algebraic methods or anything that will help us. We'll use L'Hopital's rule instead. Thus, we take the derivative of the numerator (3sin3x), times 3 because of the chain…...
Calculus
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Calculus: Parallel Lines
Parallel lines Parallel and perpendicular lines are defined as follows: Parallel lines- two or more lines that do not intersect with each other, no matter what distance you move them. Perpendicular lines- two or more lines that intersect at a 90 degree angle. What if we don't have a line that's exactly equal to 0? Rephrasing, instead of x + 1/2 y = 0, what if we had x + 1/2 y = 1? Consider having the line x plus…...
Calculus
Finding the Rotated Vector: Solving for w in Various Cases
Rotating a Vector Here's the problem: Let v denote a vector that has initial position v1 and final position v2. We know these two numbers. Now suppose we rotate v counterclockwise by an angle theta. The result is a new vector, denoted by w, that also has initial position v1 and final position v2. Let's say that we rotate vector v by an angle theta. If we do this, our new vector becomes w. The problem we are going to…...
Calculus
Derivatives of Exponential and Natural Log Functions
Derivatives of Exponential and Natural Log Functions We will introduce the concept of early transcendentals now, and then vou will learn more about them as we go along. We'll just incorporate them into our existing knowledge of products, quotients and derivatives. Now we will examine the derivatives of e to the x and natural log of x. Let's begin by doing e to the x. There are many ways to prove this. One definition of e is 1 plus x…...
Calculus
Tangent Lines and Instantaneous Rate of Change
Definition of Derivative A tangent line is the straight line that touches a curve at just one point. Tangent lines are central to calculus and have been since the 17th century. Today, we'll examine the problem of determining tangent lines for functions. The two fundamental questions addressed in calculus are: (1) What is the area under a curve, and (2) what is the slope of a line? In Algebra I, we learned that the slope of a function equals the…...
Calculus
Derivatives of Inverse Functions
Derivatives of Inverse Functions Let us assume that we have a function fox, and let us call it 3x - 1. We want to establish some sort of relationship between the slope of f and the slope of its inverse. To do this, we take these two functions and switch their x-variables and y-variables. This is all basic algebra. Next, we solve for y by adding x to one side of the equation and dividing by 3. After that, we…...
Calculus
Particle Motion. Example Problem 2
Particle Motion. Example Problem 2 An object moves along the y-axis such that its position is given by y(†) = t^3 - 12t^2 + 21t - 3 at what time does the object change direction? v(t)=0 y'(t)=3t^2-24t+21=0 t^2-8t+7=0 (t-1)(t-7)=0 t=1, 7 Given an object moving on the y-axis, its position is described by this equation. At what time does the object change direction? I believe you will find that the concepts of position, velocity, and acceleration-as they relate to particles--are…...
Calculus
Linear Approximation and Perpendicular Vectors
Linear approximation You already know about about functions of several variables and linear approximation Also, you are familiar with vectors. Now we'll unite those concepts. Let's review linear approximation. Here is some complicated function, fof (x,y). F(x,y) The function is complicated, but if we take a little box in the xy- plane, then inside of this box the function is well approximated by something way less difficult. It is almost equal to an expression of the form ax + by…...
Calculus
Review Critical Points
Review critical points A critical point is a point where the partial derivatives are both O. In this lecture, we will continue to explore critical points and learn how to actually decide whether a particular point is a minimum, maximum, or sadale point. There are various kinds of critical points. Local minima, local maxima, which are like that, and saddle points which are neither minima nor maxima. And, of course, if you have a real function, then it will be…...
Calculus
Calculus Basics: Limits, Functions, Derivatives, Integrals, and Series
Calculus is the study of change which focuses on limits, functions, derivaties, integrals, and infinite series. There are two main branches of calculus: differential calculus and integral calculus, which are connected by the fundamental theorem of calculus. It was discovered by two different men in the seventeenth century. Gottfried Wilhelm Leibniz – a self taught German mathematician – and Isaac Newton – an English scientist – both developed calculus in the 1680s. Calculus is used in a wide variety of…...
CalculusGeometryIsaac NewtonMathematicsPhysics
Add Math Project 2019
Experience classroom environments which are Hellenizing, interesting and meaningful land hence improve their thinking skills. Experience classroom environments where knowledge and skills are applied in meaningful ways in solving real-life problems. Experience classroom environments where expressing ones mathematical thinking, reasoning and communication are highly encouraged and expected. Experience classroom environments that stimulates and enhances effective learning. Acquire effective mathematical communication through oral and writing, and to use the language of mathematics to express mathematical ideas correctly and precisely.Essay Example on…...
CalculusLearningMathematicsProject
Applying Math to Real Life
I think that many math topics have meaning and relevancy and are dependent on the path one takes in terms of finding real world application. For example, sports is largely dependent on sports. Decisions are made based regarding playing time as well as strategy based on percentages. In baseball, there is a strong use of math. Managers have to make decisions on which pitchers to start and, especially so in games of importance, those decisions are predicated upon statistical reality.…...
CalculusIsaac NewtonMathematicsTime
Application of Geometric Sequences and Series
A sequence is a set of real numbers. It is a function, which is defined for the positive integers. The value of the function at a given integer is a term of the sequence. The range of a sequence is the collection of terms that make up the sequence. If the sequence only be defined for the positive integers up to a given integer n is called infinite sequences. If a sequence defined only for positive integers up to a…...
CalculusMathematics
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