Let the domain of x and y be all people, Let W(x): "X is a woman". M(y): "y is a man", and L(x.y): "y loves x". Then vxay. [(W(x) AM(y)) → L(x,y)]means Every man has a woman that loves him

Give an example of two functions t₁(n) and t₂(n) that satisfy the relations t₁(n) w(n²), t₂(n) = w(n²) and t₁(n) — t₂(n) = o(n²). =

J) use your answer in i to find E[Y] and Var[Y] 

hove directly that the functions f1 (x) =1. fa(x) = x, and f2(x) = x2 are linearly independent on the whole real line. n me n functions f1, f2,..., fn are said to be linearly independent on the interval I provided that the identity Cif1 + C2f2 + .. + Cnfn =0 holds on I only when (1) - W art for constants C1, C2, .., Cn• Given, f1 (x) = 1, f2(x) = x, and fa(x) = x², the identity c, f, + c,f, + ... as, + Cnfn =0 can bewritten (0 CL= (-0. The current equation involves thee unknowns, c1. cɔ. and ca. Two more equations are needed in order to determine the Values of all three unknowns. How can these two equations be determined? Select the correct choice below and fill in the answer boxes to complete your choice. %3(1.0.JW nsilanoW Insbneqabni yhoenil ons r W aA O A. Determine the first and second derivatives of the current equation, with respect to x. The first derivative is (x)s (d.p.w nablandw eT B nebnoqab hsonil en enll isat s 0.0 gebou 3(d.p .W nelaniow erfT O The second derviative is =…

) Find f(−5), f(−1), f(0), f(1), f(3), and f(5) for y = f(x)

Let R(x), C(x), and P(x) be, res pectively, the revenue, cost, and profit, in dollars, from the production and sale of x items. If R(x)= 6x and C(x) = 0.005x+ 3.5x + 70, find each of the following. a) P(x) b) R(200), C(200), and P(200) o) R'(x), C' (x), and P'(x) d) R (200), C (200), and P (200) a) P(x)= VI814 Ce esc % backsc %23 7 8. 3. 4 5 r t y e tab d. f h j 00 %24

|x² + y², x² + y² < 4, y 2 0 0, fxx(x,y) = otherwise

Given ⃗x =(−1)       (2)       (3)  y =(3)      (4)      (2) and  z =(2)               (6)               (6) Is z in the span of x and y? Justify your answer.

2. Let f(x) = 3x – 7, find a linear function g for which f (g)= I and for which f(g (x)) =x for any number x the function g is: a. g:x →+7. 3 x+7 b. g:x→- 3 7-x c. g:x→ 3 x+7 d. g:x→- 3 x-7 e. g:x→ 3