

Exercise 3.3 The x- and y-isoclines are given by a-bx-cy = d-ex - fy- 0 in int R2. These are straight lines with negative slopes. (a) If the isoclines coincide, then show that xy-k (with k = a/d) is a constant of motion. (b) If the isoclines do not intersect in int RA, one of the species (which one?) F tends to extinction (see fig. 3.1). One species, in this sense, is dominant. Fig. 3.1.
Find fz, fy and f. for the function f(x, y, z) = z?eyz
3. Consider following frame:
a. Set up formulas to calculate external reactions at A and B.
Obtain values of F(Ax) and F(Bx).
b. Draw free body diagram of member AC and calculate values of
F(Ax), F(Cx), and F(Cy).
c. Draw free body diagram of member BC. If problem is solved
right, this diagram should be balanced.
3 m 9 m 800 N-m 5 m 5 m
3 m 9 m 800 N-m 5 m 5 m
,y)-3x2-5xy + y2 find F 3. or the function (x a) f (x, y) b) fy,(xr, y) c) f(x, y)
,y)-3x2-5xy + y2 find F 3. or the function (x a) f (x, y) b) fy,(xr, y) c) f(x, y)
Algebra Let F: R- R2 be a linear transformation satisfying 0 (a) Find Fy (b) Find ker(F). In both cases you must show working to justify your answer.
Find fx, fy, and fz 5) f(x, y, z) = ln (xy)?
work. 1(a). Find fa, fy and fx for the function f(x, y, z) = xpez
2. Verify that a built-up ASTM A572 Grade 50 (Fy - 345 MPa) column with PL 205 x 25 mm flanges and PL 380 * 6 mn web is sufficient to carry a dead load of 300 kN and live load of 900 KN in axial compression. The column, having an unbraced length of 8 meters, is braced at the midpoint about the weak axts, the ends are pinned in both axes. (Use ASD, 15 pts)
Let f(x, y, z)=zxly. Find the value of the following partial derivatives. (a) f(4,4,3) (b) fy(4, 2, 4) (c) f(2,4,3)
1. Find the directional derivative of the function f(x, y, z) = 2.cy – yz at the point (1,-1,1) in the direction of ū= (1,2,3). Is there a direction û in which f(x, y, z) has a directional derivative Dof = -3 at the point (1,-1,1)?