# Help with multivariate Calculus

• am100181
In summary, the conversation discusses proving the statement max{a,b}=1/2*(a+b+|a-b|) and using this statement to show the continuity of a function h(x) defined by max{f(x),g(x)}. Additionally, it explores how to prepare for multivariate questions and provides a possible approach for solving such problems.
am100181

## Homework Statement

Show that:

max{a,b}=1/2*(a+b+|a-b|)

Hence or otherwise, show that if f,g:R ----> R are continuous, then the function h:R ----> R defined by h(x) = max{f(x),g(x)}
is also continuos.

Suppose the f:(0,inf) ---> R is differentiable and f(x) ---> 0 as x---> inf. Set g(x) = f(x+1-f(x). Prove that g(x) ---->0 and x----> inf.

## The Attempt at a Solution

How do I start attempting such questions? I am thinking of taking multivariate next sem and am wanting to prepare myself for such questions...

Thank you

Welcome to PF!

am100181 said:
Show that:

max{a,b}=1/2*(a+b+|a-b|)

How do I start attempting such questions?

Hi am100181! Welcome to PF!

Just treat the two cases a≥ b and a< b separately.

## 1. What is multivariate calculus?

Multivariate calculus is a branch of mathematics that deals with the study of functions of several variables and their derivatives. It is used to analyze situations where multiple variables are changing simultaneously, such as in physics, economics, and engineering.

## 2. Why is multivariate calculus important?

Multivariate calculus is important because it provides a framework for understanding and solving complex problems that involve multiple variables. It is essential in many fields of science, technology, and engineering, and is used to model and predict real-world phenomena.

## 3. What are some applications of multivariate calculus?

Multivariate calculus has a wide range of applications, including physics, engineering, economics, computer science, and biology. It is used to solve problems related to motion, optimization, probability, and growth, among others.

## 4. What are the main concepts in multivariate calculus?

The main concepts in multivariate calculus include partial derivatives, gradients, multiple integrals, vector calculus, and optimization. These concepts form the foundation for understanding and solving problems involving multiple variables.

## 5. How can I improve my understanding of multivariate calculus?

To improve your understanding of multivariate calculus, it is important to practice solving problems, review key concepts regularly, and seek help from textbooks, online resources, or a tutor if needed. It is also helpful to apply multivariate calculus to real-world problems to see its practical applications.

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