Question: Let [ a , b ] R be a non-degenerate closed bounded interval, and let f : [ a , b ] R be a

Let [a,b]R be a non-degenerate closed bounded interval, and let f:[a,b]R be a function. Suppose that f is zero except at one point. Prove that f is integrable and that abf(x)dx=0 .

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Autosave D () @ '? v Home Insert Draw Page Layout Formulas Data Review View Automate Module 4 Assignment v e Calibri (Body) vz v A General v w oy Paste B I Uwv A v o Conditional Format Cell o L s...

4.4.2 Find an example of a function f: [a, b] - R for some non-degenerate closed bounded interval [a, b] C R such that f is continuous and differentiable on (a, b), and that f does not satisfy the...

Can you help me with this Real Analysis problem, please?(Can you have the answer written on paper too, please? I feel like I can read it easier that way. Thank you very much!) Exercise 5.3.3. [Used...

Exercise 5.6.6. [Used in Theorem 5.7.4.] Let [a,b] R be a non-degenerate closed bounded interval, and let f : [a,b] R be a function. Suppose that f is integrable and f has an antiderivative. Let F :...

4. Find an example of a function f: [0,1] - R such that f is not continuous, but that f satisfies the conclusion of the Intermediate Value Theorem. Intermediate Value Theorem: Let [a, b] C R be a...

Decide which of the following statements are true and which are false. Prove the true ones and provide counterexamples for the false ones. a) If f is continuous on [a, b] and J := f([a, b]), then J...

Let f be continuous on a closed, bounded interval [a, b] and suppose that DRf{x) exists for all x (a, b). a) Show that if f(b) y0} satisfies f(x0) = y0...

Let f, g be continuous on a closed bounded interval [a, b] with |g(x)| > 0 for x [a, b]. Suppose that fn f and gn g as n , uniformly on [a, b]. a) Prove that 1/gn is defined for large n and fn/gn...

*8. Let I be continuous on a closed, bounded interval [a, b] and suppose that DRI(x) exists for all x E (a, b). (a) Show that if I (b) yo} satisfies...

You must show all of your work. Partial credit will be given. Calculators are allowed on this exam Problem 1. Let f(0) = 02 cos . (a) Find the lincar approximation of f(0) at 0 = T Proble (9)Make a...

Suppose that I is a nondegenerate interval, that f : I R is differentiable, and that f'(x) 0 for all x I. a) Prove that f-l exists and is differentiable on f(I). b) Suppose further that I is a...

Gator Corporation manufactures several types of accessories. For the year, the gloves and mittens line had sales of $498,000, variable expenses of $365,000, and fixed expenses of $144,000. Therefore,...

Port Townsend Cedar Company acquired a saw for $34,000 with an expected useful life of 5 years and a $2,000 expected residual value. Prepare a tabular comparison (similar to Exhibit of the annual...

Novelt ech successfully delended one of its patents ( Patent XIT ) from infingemene, incuming lingal costs of $ 5 0 . 0 0 0 . Patent XT had an orginal estimated useful life of 1 5 years. At the time...

Exercise 10-5 Working Backwards from Labor Variances [LO10-2] The auto repair shop of Quality Motor Company uses standards to control the labor time and labor cost in the shop. The standard labor...