Purchase Solution

Continuous function

Not what you're looking for?

Ask Custom Question

34.12 Show that if f is a continuous real-valued function on [a,b] satisfying
b
∫ f(x)g(x) dx = 0 for every continuous function g on [a,b], then f(x) = 0 for
a
all x in [a,b].

Attachments
Purchase this Solution
Solution Summary

This is a proof regarding a continuous real-valued function.

Solution Preview

Please see the attachment.

We need to use the following properties of integrals. Suppose is integrable on the interval .
P1: If for any , then
P2: For any , we have
P3: If for any , then .

Suppose is a continuous function on and satisfies for every continuous ...

Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

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.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

View More Free Quizzes
Related BrainMass Solutions

  • Properties of Continuous Functions

    To prove this we use the property of continuous function which says the ratio of two continuous functions is again a continuous function at all those points where the denominator is not zero.

  • existence and value of the limit of a function

    If a function is continuous at every point in an interval, then we say that the function is continuous in that interval and if a function is continuous in any interval, then we simply call it a continuous function.

  • Fourier Series of a Periodic Fuction : Convergence

    (h) Its Fourier series converges to all points since this function is continuous (i) Its Fourier series converges to all points in since this function is continuous .

  • some questions on limit and continuity

    c from the left are equal and the function is continuous.

  • properties of the Stone-Weierstrass Theorem

    b) If c) if d) if Then any continuous function K to R can be uniformly approximated on K by functions in A. ] Show that any continuous function on to R can be uniformly approximated by functions of the form where .

  • Convex and lower semi-continuous functions

    b) A function is lower semi-continuous if it is lower semi-continuous at every point in its domain. In , the function is clearly continuous (it is a quotient of continuous functions) and so is also lower semi-continuous.

  • Continuous Functions and Intervals

    202805 Continuity -State the intervals on which the function is continuous (see attached graph) State the intervals on which the function is continuous (see attached graph) The function shown in the figure is not continuous anywhere.

  • Limits and Continuous Functions

    Is the function f(x) continuous at x=0 from the right? is the function f(x) continuous at x = 0? Explain. Please see the attached file for the complete solution. Thanks for using BrainMass.

  • Discontinuous function

    so the function is not continuous when x=2 This shows how to list all the values of x for which a function is not continuous.

View More Related Solutions