4. Let f(x) = (in x)? (a) Find the average value of f on the interval...
=3. (2 points) Let f(x) dx (a) What is the average value of f(x) on the interval from x = 0 to x = 4? average value - (b) If f(x) is even, find each of the following: 1-4 f(x) dx = the average of f(x) on the interval x--4 to x 4 = (c) If f(x) is odd, find each of the following: 1-4 f(x) dx = the average of f(x) on the interval x =-4 to x =...
6. Find the average value for of the function f(x) = cost over the interval [0.21] and find c such that f(c) equals the average value of the function over [0, 2x].
11. (4pts) Find the average value of the function f(x) = 4.1 over the interval [3,5]. 12. (4 points) Let Pn := {20,21, ..., 2n} a partition of the interval [3,5); 20 = 3, 2n = 5, by || P1 || we denote the norm of the partition. Define Alk = xx – Ik-1 and cx = 3.2k-1 + 2 tk. What integral equals the following limit n lim || P1102 k=1 Ĉ(2) Alk C +
Find the average value of the function on the given interval f(x)=e^x/7 IN DECIMAL FORM Find the average value of the function on the given interval. f(x)=eX/7: [0, 1] The average value is . (Round to three decimal places as needed.)
4. Let f(x)= (x-4)" - (n)(n+1) a) Find the interval of convergence of f. b) Find f'(x), and determine its interval of convergence,
9. Find the average value of f(x) = 3x2 - 2x on the interval [1,4]. (8 Points) Hint: Use the formula: favo = 6-a Srca) dx
Find the average value of the function f(x) = x3 + 4 on the interval [2,4].
5. (Expected value) Let X be a continuous random variable with probability density function S2/a2 if 1 2, f(x) elsehwere. 0 Find the expected value E (In X). Hint: Integration by parts
5. Let X have a uniform distribution on the interval (0,1). Given X = x, let Y have a uniform distribution on (0, 2). (a) The conditional pdf of Y, given that X = x, is fyıx(ylx) = 1 for 0 < y < x, since Y|X ~U(0, X). Show that the mean of this (conditional) distribution is E(Y|X) = , and hence, show that Ex{E(Y|X)} = i. (Hint: what is the mean of ?) (b) Noting that fr\x(y|x) =...
2. Let 6 marks (a) Find f(x),f"(x), and f"(x). (b) Find the second order Taylor expansion of f at 1, namely f(r) = ao + ala-1 ) + a2(z-1)2 + R2(x), where Ra is the remainder. You should find ao, a, a2, and R(p). 8 marks that the error in this estimation (i.e., R2(0.9)1) is at most 10-3. 6 marks (c) Use the Taylor expansion found above to estimate the value of f(0.9). Show Find f(x), f"(), and f" (b)...