Show that if f(x) is integrable on every interval of real numbers, and if a and b are real numbers with a < b, then a. f(x) dr and f(x) dx both converge if and only if S f(x) dr and , f(x) dx both converge. b. fx) de + f(x) dx = f f(x) dx + f(x) dx when the integrals involved converge.

Q: 'he function f: E → R is uniformly continuous if

A: We have to find the answer using the definition of uniform continuity.

Q: Let f (x, y) = 1 5+√x²+y²-1 Then range of f is:

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Q: Let's assume that f(x)= r²+c* I c-16 g(x, a) = a* x² + ar Find a such that the following error is…

A: Given that where            That is  Also, given that

Q: Evaluate SIL. dydzdke, where E = {(x,y,z): (2+z12<x< 2, - (4 - z)2sy <(4 -2)12, 3<z 58}.

A: Given: The given integral is ∫∫∫Rdydzdx The given intervals are (y2+x2)12≤x≤2, -(4-z2)12≤y≤(4-z2)12,…

Q: If f is a function that is continuous on the open interval (1, 4), then f is continuous at x = 3.…

A: Given: If f is a function that is continuous on the open interval (1,4), then f is continuous at…

Q: Evaluate fv*+1dx x2 A. 를 (1 +즐)를 -를 (1+ 즐)를 :. 를 (1-즐)를 -를 (1-2)를 + C + C + C D. + C Evaluate the…

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Q: If a and b are real numbers and f(x) and g(x) are differentiable functions such that fla)=g(a)=1,…

A: Introduction: The by parts method is a method to determine integration. When the integrand is given…

Q: Show that f(x) = 2a + 3b is continuous, where a and b are constants

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Q: 6. Prove that f(x)=√x is continuous for all x ≥ 0.

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Q: Let \n (xy) + y ² = x6+3 find dy ax

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Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b - 1<x< 1, 3 x21 Continuous at x=1

A: From  the given problem:   gx=-2x≤-1ax-b-1≤x&lt;13x≥1     As we know that a function f(x) is…

Q: Since f(x) is continuous between a and b, the function needs to cross the x-axis. O TRUE O FALSE O…

A: Given fx is continuous between a and b

Q: O Let f(x, y) = (5æ – y)°. Then -

A: We can find the required partial derivatives as below

Q: Does f(x) 1-V1-x² continuous on the interval [-1, 1]?

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Q: Suppose that f is continuous at (5, 2) and that f(5, y) = y³ for y# 2. What is the value ƒ(5,2)?…

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Q: 6) Let F(x,y,z) = and f(x,y,z)= || F(x,y,z)||. Show that V(Inf) = F/f².

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Q: 2. Let X - Uniform[0, 1]. Calculate E(E(X)) and Var(Var(X)).

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