Determine k, so that ƒx,y(x, y) = [k(x+y) 0

Q: Suppose that g is a continuous function. Find the general solution of y" – y = g(t).

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Q: agrange's mea 2x in 0,

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Q: Suppose that f(x) is a continuous function on [a , b] and F(x)= | f(t) dt a Part 1 of the…

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

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Q: 3. Let X be the amount of an insurance claim which has following pdf: Kx? (4 -x), 0 <x < 2 (x) %3D…

A: f(x)=Kx2(4-x) ,      0&lt;x&lt;20,            otherwise

Q: Let the PDF of X be given by f(x) = 4 x³, 0<x,1 0 otherwise If Y = 1-3 x², Use transformation…

A: The PDF of  is given by Given transformation

Q: Show that, for any constant k, f(x)' dxL k f'(x) k

A: To show: For any constant k, ddxf(x)k = f'(x)k

Q: 2) Find a value of c for which f (x) is a pdf on the f(x) = cx + x², [0. 1]

A: Introduction ∫-∞∞fxdx=1 The total area under the curve fx of pdf is 1.

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

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Q: Suppose that the p.d.f. of X is as given f(x) = 3(1-x)2 for 0<x<1 and 0 otherwise Find the pdf of…

A: If Y=g(X) is the transformation then the PDF of Y is given by; fY(y)=fX(g-1(y))ddyg-1(y)

Q: At what points is the function is continuous y=|2x-1| +4sin(2x)

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Q: 3. Let X be the amount of an insurance claim which has following pdf: Kx (2-x), 0<x <3 f(x) = 0,…

A: Given : The pdf of random variable x is : f(x)=Kx2(2-x),0,x&lt;30,elsewhere We want to find value of…

Q: Suppose that y is a function of u, u is a function of x, and u = -1 when x = 2. If du/dx|x=2 = 3 and…

A: Solution

Q: Define. Show that h is continuous at x = 0 but h' (0) does not exist

A: Function is said to be continuous at a point x=a, when the function is defined at a and the limit of…

Q: Decide whether or not the real function In (eon 2) I+0, = (1) 1= 0, is continuous at r = 0.

A: The given function is fx=ln cos2x2x2     if  x≠0-1                if  x=0. Compute the limit…

Q: 3. Let X be the amount of an insurance claim which has following pdf: Kx2(2-x), 0<x <3 0 <x f(x) =-…

A: It is given that, x be the amount of claim with pdf fx = Kx2 2-x,0&lt;x&lt;30,elsewhere

Q: Suppose that a continuous function g satisfies: g(x)dr = 30 and g(2x)dx = 3. 0. 2 Find r9(3x²)dx.

A: Suppose that a continuous function g satisfies: ∫03gxdx=30 and ∫06g2xdx=3. The, we have to find the…

Q: The function f(x) = Ei-1 Cix;| is piecewise linear and convex. True O False

A: Step:- 1 Convex piece-wise Linear: - A function f: ℝn→ℝis a convex piece-wise linear if there exist…

Q: Give an example of a differentiable function ƒ whose first derivative is zero at some point c even…

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Q: Prove that f (z) =zz is nowhere analytic

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Q: Let f(x)= (x²e* )/2 for x> 0, and zero otherwise. Show that f(x) is a pdf. b. Find the mean. Hint:…

A: The given function is:

Q: Suppose that f is continuous at (4, 6) and that f(4, y) = y' for y + 6. What is the value f(4, 6)?…

A: Given that f is continuous at 4,6 and that f4,y=y3 for y≠6. We have to find the value f4,6. Since,…

Q: Assume ƒ is a continuous on [2, 4],, and ƒ(2)= 4. Evaluate ƒ(4).

A: we have been given that f is continuous on [2,4] and f(2)=4. we have to evaluate f(4). the given…

Q: d dx y' z' y" z"

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Q: et f(x,y)= x^2-xy+y^2-y   what are the min and max values of Du f(1,-1)?

A: Given :  f(x,y) = x2-xy+y²-y  To find :  Maximum and minimum values of directional derivative at…

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 4x/3 on the interval [0,…

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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: The interval over which the function f(x) = becomes continuous is %3D x+8 (-3, 0) (-3, 3) (-00,…

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Q: a red coin as a 1 on one side and a 3 on the other. a blue coin has a 0 and 1. let X represent the…

A: Given Red coin→ 1,3 Blue coin→ 0,1 X→ Total of both coins Y→ No. flipped on the blue coin

Q: The function(x)= is concave down on which interval?

A: Given: f(x)=1x2+1

Q: 2(x1|x2) = c1¤1/x3, 0 < x1 < x2 < 1, zero elsewhere, and f2(x2) = c2x½, 0 < x sewhere, denote,…

A: *Answer:  Give that 2. Let f12 (12) = C₁x₁/x²2, 0 &lt; x₁ &lt; x2 &lt; 1, zero elsewhere, and f2(x2)…

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 16/x on the interval [0,…

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Q: Differentiate the function. P'(W) = P(w) = 6w² - 4w+2 √w W

A: To differentiate the following function.