Purchase Solution

Differential equations

Not what you're looking for?

Ask Custom Question

Define:
f(x) = (x^2)sin(1/x)+x if x doesn't equal 0
f(x) = 0 if x=0

Prove that the function f:R-> R is differentiable and that f'(0)=1. Also prove that there is no neighbourhood I of 0 such that the function f:I->R is increasing.

Purchase this Solution
Solution Summary

This is a proof regarding differentiability of a function.

Solution provided by:
Chris Busu, PhD (IP)
Education
  • BSc, University of Bucharest
  • MSc, Ovidius
  • MSc, Stony Brook
  • PhD (IP), Stony Brook
Recent Feedback
  • "Thank you "
  • "Thank You Chris this draft really helped me understand correlation."
  • "Thanks for the prompt return. Going into the last meeting tonight before submission. "
  • "Thank you for your promptness and great work. This will serve as a great guideline to assist with the completion of our project."
  • "Thanks for the product. It is an excellent guideline for the group. "
Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • ordinary differential equations

    This solution highlights the difference between ordinary differential equations (ODEs), and partial differential equations, (PDEs).

  • Differential Equations of Exponential Functions

    54447 Differential Equations of Exponential Functions Differential Equation (IX): Formation of Differential Equations by Elimination Eliminate the arbitrary constants from the equation: y = Ae^x + Be^2x + Ce^3x.

  • Solving Differential Equations with given initial conditions

    343044 Solving Differential Equations with given initial conditions Please see attached Please show all work with explanations. Differential Equations 5. Solve the differential equation with the given initial conditions: 6.

  • Differential equations of all parabolas

    54452 Differential equations of all parabolas Differential Equation (XII) Formation of Differential Equations by Elimination Find the differential equations of all parabolas whose

  • Differential equations of Circles

    54455 Differential equations of Circles Differential Equation (XV) Formation of Differential Equations by Elimination Find the differential equations of all circles of radius (whatever

  • Solve Three Differential Equations

    27612 Solve Three Differential Equations Find the general solution of the following system of differential equations: i.e. 1) dx/dt = x-2y-t2 (FOR COMPLETE PROBLEMS PLEASE SEE ATTACHMENT) Given system of differential equations is (dx/dt)=x-

  • Numerical Methods for Differential Equations: Recursive Formula

    The numerical methods for differential equations for recursive formulas are examined. The differential equations are analyzed for the original equation.

  • Solving exact differential equations

    (c) Hence find the general solution of the differential equation. (See attached file for equations). Please find solution attached herewith. This solution explains how to solve Exact differential equations.

  • Differential equations

    This provides examples of working with differential equations, including classifying, writing differential equations to fit descriptions, determine whether functions and relations are solutions, and determining whether an initial value problem has a solution

  • Ode - Convert into System of Differential Equations

    The solution assists with converting into system of differential equations.

View More Related Solutions