For a convex set SC R", what is the normal cone Ng(x) of S at a point x € S?

2a) Use six rectangles to find estimates of each type for the aria under the given graph of f from x-0to X=12. i Lo (sample polnts are left endpoints) n.Ro(sample points are night endp0ints) i. Mc (sample points are midpoints.) b) Is Lc an wnderestimate or overestinate cf the true area? ) Is Re ano wnderestimate or overestimate of the true area? ) which of the numbers Le, Ro,or Ma gives the -best estimate? Gxplain. YA 8. 12

The scatter plot displays bivarlate data on the outside temperature in degrees Fahrenheit, x, and the corresponding number of beachgoers, y, at a local beach. Temperature and Beachgoers 60 50 30 20 10 55 60 65 70 75 Temperature ("F) 85 Outliers appear to be located at (66, 45) and (85, 15). | The outlier (66, 45) represents 45 beachgoers visiting the beach on a day when the outside temperature was 65°F. The outlier (85, 15) represents 15 beachgoers at the beach on a day when the outside temperature was 85°F. Perhaps on the 85° day, people attended a big event, such as a football game instead of the beach. This could explain why fewer people attended the beach. Likewise, maybe there was a special competition at the beach on the day that the temperature was 66°F. This could explain why more people went to the beach even though it was not very warm. The strong, positive, and linear association indicates that there are more beachgoers on warmer days. The general trend shows that, for…

I really need help figuring out how to do this problem, using the cheat sheet formula provided

$. flx) =3=x*, glx)= x² 4 B) (f tgl(x) domain d) Domain f) domain H) Domain

Let A = {4, 5, 7} and B = {x, y}. Let p1 and p2 be the projections of A ✕ B onto the first and second coordinates. That is, for each pair (a, b)  A ✕ B, p1(a, b) = a and p2(a, b) = b. (a) Find p1(4, y) and p1(7, x) What is the range of p1? (Enter your answer in set-roster notation.) (b) Find p2(4, y) and p2(7, x). What is the range of p2? (Enter your answer in set-roster notation.)

Please show all work

Given: y² = 2x - 2 bounded by y = x-5. The points of intersection of these two curves are {A} (9,-4); (-3,2) {B} (-9,4); (-3,2) {C} (9,4); (3,-2) {D} (-9,-4); (-3,-2)

multivariate calculus   Partially differentiate the follwoing with respect to x1 and x2

5. Show that the following orthogonal families of curves: are x² + y? : = ax, x² + y? = by