Let f EBV (Co,1]). Define F(x) = { ["f(t) dt, x € (0,1], St Lo, x = 0. Show that F E BV([0.1).

Q: Assume that f is an odd function defined on R and t e Rt. Compute

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Q: Show that the function f(z)= Im(z) is nowhere differentiable.

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Q: Let f(r) = re. Find f'(r).

A: f(x)=xex2

Q: Let fx (x) = x +b, x ∈ [−2b, 2b]. For which b is fX (x) a pdf?

A: Given,  fx (x) = x +b, x ∈ [−2b, 2b] To find the value of b for which fX (x) is a pdf.

Q: 1. Show that m*(Q) = 0, where Q is the set of rational numbers. 2. Let x e R. Then m*(A) = m*(x + A)…

A: 1)

Q: Differentiate the function. = In({ (4t+ 1)³ (4t-1)5 F'(t) = F(t) = In

A: The derivative of the function in the division form is given by the quotient rule which is given by-…

Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

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Q: consider che funceion h= w²-8.Tawei Determine dh/dt and w= St"-26

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Q: Let F(x) = x √ √2+1 dt. Find F"(1) 3

A: Given: F(x)=∫3x t2+1dt Leibniz integral rule for differentiation states that ddx∫a(x)b(x)…

Q: if r'y-- 2y + 1.

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Q: Determine which of the following pairs of functions are linearly independent. NO_ANSWER 1. f(0) =…

A: The linear dependency of functions can be evaluated using the value of the Wronskian of those…

Q: Let X ~ Exp(λ). Find F(X) and E(X).

A: Let X ~ Exp(λ)The probability density function of X is fx(x)=e-λx   ;x>0

Q: et f(z) = | t'dt. Evaluate the following.

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Q: Let f(x, y) = e"r³ Evaluate f(3, 0)

A: The function of two variables  x and y will be of the form,   The function value of this kind of…

Q: Let f(t) = 2t¹ – 3t+2eª. Then f'(t) =

A: NOTE: Refresh your page if you can't see any equations. . the given function is

Q: 3. Find all functions from X = {a,b} to Y = {p,r, t}.

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Q: Determine the n-th derivative fn) of the function f: (0, +0) → R, f(x) = x ' exp ( 1 - ), n EN

A: f(x)=1x,  f:(0, +∞)→R,…

Q: Let F(x, y) = . Evaluate (3,2) SF.. (1,-1) F.dr

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Q: Let g(z) = (z3 + (z² – 1)5) . Then the derivative of g is g'2) = A(2? + (z? – 1)9)* (cP + F z(z? –…

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Q: Find y as a function of a if y(1)=2, y(1) = 1. y = r²y" + 7xy +9y = 25,

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Q: Let F be the function given by F (x) = S" (sec² (5t) – 1) dt. Which of the following is an…

A: We have given that   F(x) = ∫2x(sec2(5t)-1)dt        ...(1). And we have to find F'(x). To find the…

Q: Determine whether the functions fi(x) = cos 3r, f2(x) = x, and f3(x) = cos² r independent on the…

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Q: Let F = (2xz+y², 2xy, x²+1), if Vf= F, find f(1, 1, 1) – f(0, 0, 0)

A: Given vector funtion and

Q: Let F(x)= | V1+P dt. Find F'(5). x,

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

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