Find constant a and b such that function f(x) = ax + b be orthogonal to...
Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax b. 8 1 -7 1 b- 1-17 a. The orthogonal projection of b onto Col A is b-(Simplify your answer) (Simplify your answer.) b A least-squares solution of Ax-b is x Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax b. 8 1 -7 1 b- 1-17 a. The orthogonal projection of b onto Col...
Consider the following functions. Ax) = xł go gcx) = x bet Find (f + g)(x). 7 + x x + 8 Find the domain of (f + g)(x). (Enter your answer using interval notation.) (-00, – 8) U(-8,00) Find (f - g)(x). 7-x x + 8 Find the domain of (f - g)(x). (Enter your answer using interval notation.) (-00, -8) U(-8,00) Find (fg)(x). 7x x+8 Find the domain of (fg)(x). (Enter your answer using interval notation.) (-00, -8)...
(a) Find all values of a > 0 and BER such that the function cos(ax)-cos(x) for < 0, f(x) = {B for x = 0, In(1+o.r) for x > 0, is continuous at x = 0.
4. We saw in class that if A is an orthogonal matrix, then ||AX|| = ||X||. One matrix for which we know this is true is the rotation matrix, A = [cos – sin 0] sin cos a. (2 pts) Show that A is an orthogonal matrix. b. (2 pts) Since A is an orthogonal matrix, A-1 = AT. Show that AT can be written as cos 0 – sino w does the angle o relate to the angle ?...
Find the constant a such that the function is continuous on the entire real line. f(x) = [ 5x2, x 21 ax - 5, x < 1 a =
(a) The wave functions f(x) and g(x are normalized and orthogonal. This means that the wave functions (x) and g(x) satisfy: un-r.dz,(zrno-1, Glg) _ Γ.dzdarg(x)-1 uw-r.dararga)-@-Γ.drdar rn-un and (4.2) Find the normalization constant N for the wave function that is a superposition of these(x) af(x)+bg( where a and b are complex valucd constants (b) Now find the normalization for the superposition ф(x) af(x) + bg(x), but take the functions f and g to be normalized but not orthogonal with their...
Find the exponential function f(x)=a^x whose graph is given. Find the exponential function f(x) = ax whose graph is given. f(x) y 20 (2, 16) 15 10 5 -3 -2 - 1 2 3
(b) (i) Given the function f(x,y)= xe' + 3x, find two unit vectors who are orthogonal to the gradient of f at the point P(3,0). (7 Marks) (ii) In which direction does f(x,y)= xey + 3x increase most rapidly at the point P(3,0)? What is the maximum rate of change at that point? (3 Marks)
Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax b 1-61 11-6 a. The orthogonal projection of b onto ColA is(Simplify your answer.) Enter your answer in the answer box and then click Check Answer part remaining
7. (Lesson 3.5) Let S(x)=-8x+16, if x53 [ax+b, if x>3. Find a and b such that the function(x) is differentiable everywhere. (HINT: First use differentiability to find a. Then use continuity to find b.) M 8 . (Lesson 3.6) Memorize the following integration formulas, then practice using them. Power Rule: If n*-1, then ſx"dx = --***!+C Constant Multiple Rule: ſk. (x)=k[ /[x]cle Sum/Difference Rule: (x)£g(x)}!x = 5 /(x)det g(x) (b) f(6x–3Vx+dr = — (a) dr = — 9. (Lesson 3.6)...