let f be the function on [0,1] given by f(x) = 1 if x is different...

let f be the function on [0,1] given by f(x) = 1 if x is different of 1/2 and 2 if x is equal to 1/2

Prove that f is Riemann integrable and compute integral of f(x) dx from 0 to 1 Hint for each epsilon >0 find a partition P so that U_p (f) - L_p (f) <= epsilon

Expert Solution

Colby Messinger answered 1 year ago

1. (a) Throughout Question 1 part (a), let f be the function given by f(x, y)...

1. (a) Throughout Question 1 part (a), let f be the function given by f(x, y) = 6+x^3+y^3−3xy. (i) At the point (0, 1), in what direction does the function f have the largest directional derivative? (ii) Find the directional derivative of the function f at the point (0, 1) in the direction of the vector [3, 4] . (iii) The function f has critical points at (0, 0) and at (1, 1). Classify the natures of these critical points...

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Let ∬[a,b]×[c,d]f(x,y)dA denote the integral of f(x,y)over the region with a≤x≤b and c≤y≤d. Find ∬[0,1]×[0,1]f(x,y)dA given...

Let ∬[a,b]×[c,d]f(x,y)dA denote the integral of f(x,y)over the region with a≤x≤b and c≤y≤d. Find ∬[0,1]×[0,1]f(x,y)dA given the following: ∬[0,1]×[1,5]f(x,y)dA=2, ∬[1,2]×[0,1]f(x,y)dA=−1, ∬[1,2]×[1,5]f(x,y)dA=4, and ∬[0,2]×[0,5]f(x,y)dA=3. Group of answer choices 2 -2 8 0 None of the above.

5) Let the function f : ℝ3 → ℝ3 be given by f(x, y, z) =...

5) Let the function f : ℝ3 → ℝ3 be given by f(x, y, z) = (2x + 2y, 2y + 2z, z + x). a) Prove that f is one to one and onto b) Find the inverse of f, i.e., f−1.

let p3x be the third order polynomiol interpolatign function f(x)=sin(x) at 0,1/3,2/3,1 show that for any...

let p3x be the third order polynomiol interpolatign function f(x)=sin(x) at 0,1/3,2/3,1 show that for any x in [0,1] we have f(x)-p3(x), or equal to 1/54

Let f be a continuous function on the closed interval [0,1] with a range also contained...

Let f be a continuous function on the closed interval [0,1] with a range also contained in [0,1]. Prove that f that there exists an x in [0,1] such that f(x)=x. Is the same explanation still valid if f is not continuous?

Question 1 Let f be a function for which the first derivative is f ' (x)...

Question 1 Let f be a function for which the first derivative is f ' (x) = 2x 2 - 5 / x2 for x > 0, f(1) = 7 and f(5) = 11. Show work for all question. a). Show that f satisfies the hypotheses of the Mean Value Theorem on [1, 5] b)Find the value(s) of c on (1, 5) that satisfyies the conclusion of the Mean Value Theorem. Question 2 Let f(x) = x 3 − 3x...

For the given function f(x) = cos(x), let x0 = 0, x1 = 0.25, and x2...

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Let f(x, y) be a function such that f(0, 0) = 1, f(0, 1) = 2,...

Let f(x, y) be a function such that f(0, 0) = 1, f(0, 1) = 2, f(1, 0) = 3, f(1, 1) = 5, f(2, 0) = 5, f(2, 1) = 10. Determine the Lagrange interpolation F(x, y) that interpolates the above data. Use Lagrangian bi-variate interpolation to solve this and also show the working steps.

Let X1,X2,...,Xn be i.i.d. (independent and identically distributed) from the Bernoulli distribution f(x)=p^x(1-p)^1-x, x=0,1,p∈(0,1) where p...

Let X1,X2,...,Xn be i.i.d. (independent and identically distributed) from the Bernoulli distribution f(x)=p^x(1-p)^1-x, x=0,1,p∈(0,1) where p is unknown parameter. Find the UMVUE of p parameter and calculate MSE (Mean Square Error) of this UMVUE estimator.

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