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Calculus and Analysis

Calculus is a branch of Mathematics which examines change. It has two major disciplines: differential and integral calculus, with one being concerned with rates of change, while the other focuses on the accumulation of quantities. Thus, it can be seen that the applicability of this study extends into economics, engineering as well as any science.

Although Calculus does not stand apart from Algebra, both of these branches can be used to solve different problems. Algebra deals with structures utilizing letters and symbols to represent specific relationships between each other. However, since the relationship is fixed, it may not be applicable to use algebra to solve problems dealing with continuously changing relationships. Thus, calculus in this context can be a very useful as there are many non-theoretical relationships which rarely stay the same.

Exploring the basic terminology, a derivative is a measure of how the output of a specific function, which is not limited to y or f(x), changes as the input changes. An integral, also known as an antiderivative, is a function F whose derivative is the given function f. Both of these form the basic tools of calculus with numerous applications in everyday life. Thus, understanding basic Calculus may prove to be a practical tool for anyone.

Categories within Calculus and Analysis

Basic Calculus

Postings: 542

Basic Calculus refers to the simple application of both differentiation and integration.

Functional Analysis

Postings: 283

Functional Analysis refers to the study of vector spaces and their properties.

Complex Analysis

Postings: 571

Complex Analysis refers to the study of complex numbers.

Calculus Maxima, Minima and Saddle Points

Show all work 1. Determine the exact value for each of the following limits: a. b. 2. Determine derivatives (with respect to x) for the following: a. b. c. d. Determine for e. Determine the partial derivative with respect to x for 3. Integrate the following: a. b. c. 4. For the fun

Math Homework

MATH 141 Homework Due Dec 2 Name : Solve the following linear programming problem using a graphical method A company makes two puddings, vanilla and chocolate. Each serving of vanilla pudding requires 2 teaspoons of sugar and 25 fluid ounces of water, and each serving of cho

Value of each definite integral

Name __________________________ Math 331 Fall 2015 DIRECTIONS: Show as much work as possible within each question as I grade on both the process and the final answer. TI-89's are wonderful calculators, but they don't show me if you know anything about calculus! Show all work. 1. (6 pts each) Determine the following ant

Trigonometric equations and angle between vectors.

Question #1: You used Pythagorus' theorem to determine whether or not a triangle was a right triangle. The sides of the triangle are: a = sqrt(416), b = sqrt(601), and c = sqrt(1009) so that a2 + b2 did not equal c2. Thus it is not a right triangle. Let the α, β, γ be the angles of the triangle across from sides a, b, c

Period of a Fraction

From what I have seen, the longest length of a repeating sequence for an irrational number is c-1 for a=b/c. This occurs when c is a prime. How does one prove this? Can you give mathematical proof for this? Here is a link to the problem being discussed: http://boards.straightdope.com/sdmb/showthread.php?t=720360

Application of L'Hopital's Rule

Task: Graph the f(x) = e^2x - 1/x Verify the Limit x→0 f(x) meets the criteria for applying L'Hopital's Rule Find the Limit x→0 f(x) Explain why L'Hopital's Rule cannot be used to find the limit of Lim x→0 e^2x/x

Solutions for intervals

Find the solutions for the attached integrals Please see attached and show step by step, thanks.

General solutions and summation

Please find the attached file. I am requesting detailed answers for all the questions. All of the questions are calculus-based and include solving for general solutions and solving summation problems.

Angular and linear velocity

In the year 1930s, some trucks used a chain to transmit power from the engine to the wheels. Suppose the drive sprocket had a diameter 6 in., the wheel sprocket had diameter 20in., and the drive sprocket rotated at 300 rev/min. a) Find the angular velocity of the drive sprocket in radians per second. b) Find the liner velocity

Effects of Data Changes Using Least Squares Method

Watch: http://academicearth.org/lectures/least-squares and/or view: http://www.efunda.com/math/leastsquares/leastsquares.cfm Consider the following dataset: (20,525) (17,57) (10,19) (9,18) (7,14) (16,41) (3,5) (5,10) (10,23) (12,24) (9,15) (20,571) (18,102) (16,56). Calculate a best fit equation using the Least Squares

Complex variables questions

Please answer the attached questions and show the necessary steps for finding the value with your wonderful explanations!

Contours

Please show the steps and the graphs for problems 2 through 6. Thank you.

Graphing Functions and Continuity

Graph the function for -2 < x < 4. Check the continuity of f(x) at x = 0 and x = 2, making sure you address all the conditions for continuity. Please see attached, and if you could show the answer step by step, thanks.

Graphing and Labelling Functions

(i) Graph the function f(x) = sqrt(x). (ii) Hence, using translation etc., graph f(x) = 2-sqrt(4-x). Show and label intermediate graphs.

Assorted Calculus Questions

Below are the graphs of four functions. Which function is invertible? Set up the integral for the length of the smooth arc y = e x on [0, 10]. What is the area of the triangle bounded by the lines x = 1, y = x − 1, and y = 3 − x ? Suppo

cooling and leaking process mathematical model

1. A heated object is allowed to cool in a room temperature which has a constant temperature of To. a. Analyse the cooling process. b. Formulate mathematical model for the cooling process. 2. At time t= 0 water begins to leak from a tank of constant cross-sectional area A. The rate of outflow is proportional to h, the d