5. A steady state solution to the problem Su₁(x, t). = 1 10 u(0,t) = 1, Uxx(x, t)+x+1, 0 0, u(2,t) = 3, u(x, 0) = πx-x², t > 0, 0 < x <2. is a function v(x) that satisfies 0 = ·v"(x)+x+1, 0 ≤ x ≤ 2, 10 (0) = 1, v(2) = 3. ☐ Find (if possible) a steady state solution, or show that no steady state solution exits.

Find yy as a function of xx if x^2*y′′+13xy′+36y=x^9 y(1)=−2,  y′(1)=−1.

Find the derivative. 1) f(x) = V7,7x A) 67,7%)4/5 B)블7+7x)-1/5(7x6 +7) C)6 47)4/5 D) 67+7)4/5(7,6 +7) 2) y = x/10x - 8 15x - 8 A) 시10x-8 21x - 16 D) 2/10x -8 15x B) 10x-8 C) /10x-8

2 3 1. Findx and y if (x 3) (² ») (² -³) = (² y) 4 = (2 −4).

Let f (**= (x)+f(9)for real values of x and y. Iff '(0) exist %3D 2 and equals -1 and f(0) = 1, then f '(2) is equal to-

17) f(x) = 5x, x = 25

Q/IF it was AY ₁2) = -12 ℗ Y³ (2) = -12 ⒸY³ (2) = -11 Y³ (2) = -11 DÝ (2) = -13 © ²³ (2) = -13 = X+1 X-1 Y = Not of the above so y" (2)

If z is implicitly defined as a function of x and y by xy-yz+xz=0, find dz/dx. (y+z)/(y-x) (z-x)/(x-y) (y-x)/(x+5) (x-y)/(2-x)

Find y' when y²e2x = 3y + x² and y(0)=3 (A) -6 B) -4 (C) -7 D) -5

8) Suppose you are at the point (2, 1, 82) on the hill given by f(x,y) = 100-4x²-2y (where the z axis gives elevation, the y axis points north, the x axis east).Correct notation is required, units are not (13 points) (a) If you hike from the given point in the direction of = (3,4) are you going uphill or down? At what rate? (b) From the given point, in what direction is the steepest climb? (c) Using the graph of f(x,y) with the point (2,1,82) shown, explain and illustrate why your answers above are reasonable (or not).