D (x) is not integrable on [0,1]

Q: branch of z1/5 that is not continuous and positive on the imaginary axis?

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Q: Is g = {(x, y) ∈ [−5, 5] × R : x^2 + y^2 = 25} a function from [−5, 5] to R.

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Q: Let X ~ N (0, 1). Demonstrate that E (X)=0 and V (X)=1.

A: To demonstrate that E(X)=0 and V(X)=1 for a standard normal distribution X∼N(0,1), we need to…

Q: Prove that a contant ,x ,x^2 are integrable on [a,b

A: Let take a constant c I=∫abcdx=cb-a For x I=∫abxdx=12x2ab=12b2-a2

Q: the function f is not differentiable at x=0.

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Q: 4. Prove that f(x, y, z) = 2 - 1 x² + y² is continuous in all its domain.

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Q: Q2) homeomorphism. Prove or disprove: The function f: (R, T1) - (R, 13) defined by f(x) = 3x is a…

A: Clearly the given function f(x)=3x is continuous. Now we want to check whether it is bijective,

Q: (6) Are all continuous functions on ID differentiable on D?

A: we have to identify the given statement is true or not

Q: Prove that the derivativeo P(zx tJ's 4(2Xbjusiy Pirst Princiele 4(2X+)by jusing first Princiele…

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Q: Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

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Q: Show that the entire function cosh(z) takes every value in C infinitely many times.

A: The function cosh(z) is the hyperbolic cosine of z and is defined as:cosh(z)=ez+e−z2We are…

Q: Let X~U (0,0), then P(X > X²) is

A: Given that X~U0,θ fx=1θ-0=1θ, 0≤X≤θ

Q: What would be an example of a function that is not integrable on [2, 10] and why is it not…

A: Consider a function: y=1x-2……1

Q: Determine all analytic functions f on nEN. D(0, 1) satisfying f() = 1 for all

A: The identity theorem for analytic functions :The identity theorem states that if two analytic…

Q: le can define an operator * : 2'(R?) n'(R?) by defining *dx = dy and *dy = -dx, and extending…

A:

Q: Show that f = {(x, y) ∈ R × R; x = y^3} is a function from R to R

A: Given, The function f={(x,y)∈R×R ; x=y3 }   We have to show that the given function is from R to R.

Q: Give an example to show that X' need not be separable if X is separable.

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Q: Show that f(x) = 1/(1+x) is analytic on (-1, ∞).

A: To show that f(x) = 1/(1+x) is analytic on (-1, ∞), we need to show that f(x) has derivatives of all…

Q: Is the function f(x) = ( 1, x not equal 1)             ( 0, x equal 1) integrable over the interval…

A: Here, we will show that the given function is integrable. Let us take a point c ∈ (0,1).

Q: Assume that f: R→ R and g: R → R are infinitely differentiable functions. Prove the following…

A: We have given that ,  are both infinitely differentiable.We need to prove that , We will use…

Q: If fCxl is continuous on [2,7],then Si f(u) dvz f (7)-(2) True e or false?

A: we have given that f(x) is continuous on[2,7].

Q: + xln\ V 1 – x° | dx

A:

Q: Show orthogonality of the functions on the interval cos(Lx), cos(2Lx), cos(3Lx), ... -T/L≤x≤n/L and…

A: The given set is S=cosLx, cos2Lx, cos3Lx, . . .. We have to show that S is orthogonal on the…

Q: 2x3 + xy? x² + 2y4 if (x, y) # (0,0) if (x, y) = (0,0).

A: See the details solution in below

Q: Show that Alf・g) = (Adig + 2D fo@g+ f(Ag)

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Q: Which of the functions are Lebesgue integrable functions on | 0,1? [a1])? In x xIn x (i) 1+x sin T x…

A: The value of ln0 is undefined.

Q: Let f be a continuous function on R. Define F(x) = [² (2. = Evaluate F"(x). (x² – t) f(t) dt.

A: