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(7 points total) Calculator allowed. Let f(x) = -x2 + 4, g(x) = x4 + 3x3...
DO ALL PARTS PLEASE Let f and g be the functions defined by f(x) = 1...
DO ALL PARTS PLEASE
Let f and g be the functions defined by f(x) = 1 +x+7-24 and g(x) = x* -6.572 +6x + 2. Let R and S be the two regions enclosed by the graphs off and g shown in the figure above. (a) Find the sum of the areas of regions R and S. (b) Region S is the line of a solid whose cross sections perpendicular to the x-axis are squares. Find the volume of the...
4. (Calculator) Let R be the region bounded by the graphs of f(x)= 20+x-x2 and g(x)=x-5x. (a) Find the area of R. (...
4. (Calculator) Let R be the region bounded by the graphs of f(x)= 20+x-x2 and g(x)=x-5x. (a) Find the area of R. (b) A vertical line x k divides R into two regions of equal area. Write, but do not solve, an equation that could be solved to find the value of k (c) The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are isosceles right triangles with the hypotenuse...
17. MULTIPLE CHOICE Let f(x) = x4 - 3x3 + 5x - 3. Use synthetic substitution...
17. MULTIPLE CHOICE Let f(x) = x4 - 3x3 + 5x - 3. Use synthetic substitution to find f(-2). F 37 H -21 G 27 I -33 Given a polynomial and one of its factors, find the remaining factors of the polynomial. 18. 2x3 + 15x2 + 22x – 15; x + 5 19. 23 - 4x2 + 10x - 12; x - 2
5. (a) (5 points) Let R F[x] for a field F. Let f, g E R...
5. (a) (5 points) Let R F[x] for a field F. Let f, g E R be nonzero. Prove that (f(x)) = (g(x)) if and only if g(x) = af(x) for some constant a E F. (b) (5 points) Let R be any ring. Prove that the nilradical Vo is contained in the intersection of all prime ideals.
5. (7 points) Let f: R3 → R be the function f(x,y,z) = x2 + y2...
5. (7 points) Let f: R3 → R be the function f(x,y,z) = x2 + y2 +3(2-1)2 Let EC R3 be the closed half-ball E = {(x, y, z) e R$: x² + y2 +< 9 and 2 >0}. Find all the points (x, y, z) at which f attains its global maximum and minimum on E.
3. Let {X1, X2, X3, X4} be independent, identically distributed random variables with p.d.f. f(0) =...
3. Let {X1, X2, X3, X4} be independent, identically distributed random variables with p.d.f. f(0) = 2. o if 0<x< 1 else Find EY] where Y = min{X1, X2, X3, X4}.
Let g(x) =3x + 5 and f(x) = x2 + 2x – 7 . Find f(g(x)).
Let g(x) =3x + 5 and f(x) = x2 + 2x – 7 . Find f(g(x)).
1. (25 points) Let f (x, y) = x4 - 4xy + y2 (6 points) Find...
1. (25 points) Let f (x, y) = x4 - 4xy + y2 (6 points) Find fr.fy a. b. (9 points) Find fxx fry, fry c. (6 points) Find all critical points.
1. (25 points) Let f (x, y) = x4 - 4xy + y2 (6 points) Find fr.fy a. b. (9 points) Find fxx fry, fry c. (6 points) Find all critical points.
(5 points) Find area enclosed by f(x) = x+ + 128 and g(x) = 160 –...
(5 points) Find area enclosed by f(x) = x+ + 128 and g(x) = 160 – x4. Answer:
Let > 0 and let X1, X2, ..., Xn be a random sample from the distribution with the probability density function f(x;...
Let > 0 and let X1, X2, ..., Xn be a random sample from the distribution with the probability density function f(x; 1) = 212x3 e-tz, x > 0. a. Find E(XK), where k > -4. Enter a formula below. Use * for multiplication, / for divison, ^ for power, lam for 1, Gamma for the function, and pi for the mathematical constant i. For example, lam^k*Gamma(k/2)/pi means ik r(k/2)/n. Hint 1: Consider u = 1x2 or u = x2....
DO ALL PARTS PLEASE
Let f and g be the functions defined by f(x) = 1 +x+7-24 and g(x) = x* -6.572 +6x + 2. Let R and S be the two regions enclosed by the graphs off and g shown in the figure above. (a) Find the sum of the areas of regions R and S. (b) Region S is the line of a solid whose cross sections perpendicular to the x-axis are squares. Find the volume of the...
4. (Calculator) Let R be the region bounded by the graphs of f(x)= 20+x-x2 and g(x)=x-5x. (a) Find the area of R. (b) A vertical line x k divides R into two regions of equal area. Write, but do not solve, an equation that could be solved to find the value of k (c) The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are isosceles right triangles with the hypotenuse...
17. MULTIPLE CHOICE Let f(x) = x4 - 3x3 + 5x - 3. Use synthetic substitution to find f(-2). F 37 H -21 G 27 I -33 Given a polynomial and one of its factors, find the remaining factors of the polynomial. 18. 2x3 + 15x2 + 22x – 15; x + 5 19. 23 - 4x2 + 10x - 12; x - 2
5. (a) (5 points) Let R F[x] for a field F. Let f, g E R be nonzero. Prove that (f(x)) = (g(x)) if and only if g(x) = af(x) for some constant a E F. (b) (5 points) Let R be any ring. Prove that the nilradical Vo is contained in the intersection of all prime ideals.
5. (7 points) Let f: R3 → R be the function f(x,y,z) = x2 + y2 +3(2-1)2 Let EC R3 be the closed half-ball E = {(x, y, z) e R$: x² + y2 +< 9 and 2 >0}. Find all the points (x, y, z) at which f attains its global maximum and minimum on E.
3. Let {X1, X2, X3, X4} be independent, identically distributed random variables with p.d.f. f(0) = 2. o if 0<x< 1 else Find EY] where Y = min{X1, X2, X3, X4}.
1. (25 points) Let f (x, y) = x4 - 4xy + y2 (6 points) Find fr.fy a. b. (9 points) Find fxx fry, fry c. (6 points) Find all critical points.
1. (25 points) Let f (x, y) = x4 - 4xy + y2 (6 points) Find fr.fy a. b. (9 points) Find fxx fry, fry c. (6 points) Find all critical points.
(5 points) Find area enclosed by f(x) = x+ + 128 and g(x) = 160 – x4. Answer:
Let > 0 and let X1, X2, ..., Xn be a random sample from the distribution with the probability density function f(x; 1) = 212x3 e-tz, x > 0. a. Find E(XK), where k > -4. Enter a formula below. Use * for multiplication, / for divison, ^ for power, lam for 1, Gamma for the function, and pi for the mathematical constant i. For example, lam^k*Gamma(k/2)/pi means ik r(k/2)/n. Hint 1: Consider u = 1x2 or u = x2....
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