Problem 2. let v = c([−π, π]) and define hf, gi = r π −π f(x)g(x)dx . as in the latest lab, we can actually prove that the set { √ 1 π sin(kx)}k∈n is an orthonormal set in the infinite dimensional space v (you do not have to prove any of these). use the exercise above and the function f(x) = x to prove x[infinity] k=1 1 k 2 ≤ π 2 6 hint: let ek = √ 1 π sin(kx), and calculate ck = hf, eki = √ 1 π r π −π x sin(kx)dx. remark: as noted above, we can actually have equality!

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

i believe that the slope of the line is -5

step-by-step explanation:

step by step solution :

step   1   :

1.1     4 = 22

(4)3 = (22)3 = 26

equation at the end of step   1   :

  ((23) • 26)2

step   2   :

equation at the end of step   2   :

  (23 • 26)2

step   3   :

final result :

  218

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