y = V14x2 (3x3 – 2) 4x2 can be written as (4x2)1/4, hence the Product Rule...
Solve the problems: 1. x2 x33. 2. 2x, + 2x1 + 4x2-3x3 → min. 8x1 3x2 + 3x3 3 40, x2 20. 3. xi + X2 = 1, x120, x120. Solve the problems: 1. x2 x33. 2. 2x, + 2x1 + 4x2-3x3 → min. 8x1 3x2 + 3x3 3 40, x2 20. 3. xi + X2 = 1, x120, x120.
5. A function f has Taylor series (at 0) f(x)=0+2x+ 4x2/2! + 3x3/3!+... Assume f−1 exists. Find as much of the Taylor series of f−1 (at 0) as you can. (Since you only know the first few terms of the Taylor series for f, you can only figure out f−1. (Hint: There are two ways of doing this problem. One is get the derivatives of f−1 from knowing the derivatives of f; we talked about the first derivative in January...
8. Minimize z - 8x1 + 6x2 + 11x3 subject to 5x1 x2 + 3x3 s 4 5x1 + x2 + 3x3 2 2 2x, + 4x2 + 7x3 s.5 2x1 + 4x2 + 7x3 2 3 X1 + X2 + X3 = 1 (a) State the dual problem. (b) Solve both the primal and the dual problem with any method that works. (c) Check that your optimal solutions are correct by verifying they are feasible and the primal and...
4. Use Inverse method to solve the system and verify your result using Cramer's rule. 2x-y+3z = 9, x+y+z=6,x-y+z=2. [15 Marks 5. Show that the equations X1 + X2 + x,-6, x1 + 2x2 + 3x3 = 14, x1 + 4x2 + 7x3-30 are [10 Marks] consistent and solve them.
Previous Problem Problem List Next Problem (1 point) Suppose that f(x) and g(x) are given by the power series f(x) 55x +3x2 + 3x3+... and g(x-643x + 4x2 + 3x3 + By multiplying power series, find the first few terms of the series for the product h(x) -f(x) .gx)cccx2 +c3 со 30 c115 C212x C39 Note: You can earn partial credit on this problem. Previous Problem Problem List Next Problem (1 point) Suppose that f(x) and g(x) are given by...
5 4 3 2 1 -2 9 10 -] The graph above can be written as y = f(t)h(t – a) + g(t)h(t – b). Recall: h(t - a) is the unit step function shifted to the right a units. Where f(t) - g(t) = b = Submit Question
Let A = Construct a 4x2 matrix D, using only 1 and 0 as entries, such that AD = I2. Is it possible that CA =I4 for some 4X2 matrix C? Explain. Is it possible that CA = I4 for some 4 x 2 matrix C? Explain. Choose the correct answer below. A. No, because neither C nor A are invertible. When writing lm as the product of two matrices, since lm is invertible, those two matrices will also be invertible. B. Yes, because...
Example 3.5-2 (Infinite Number of Solutions) Maximize z = 2xy + 4x2 subject to *'y + 2xy = 5 X1 + X2 5 4 *1,*220 Figure 3.9 demonstrates how alternative optima can arise in the LP model when the objec- tive function is parallel to a binding constraint. Any point on the line segment BC represents an alternative optimum with the same objective value z = 10. The iterations of the model are given by the following tableaus.
(a) Find the slope m of the tangent to the curve y = 2 + 4x2 − 2x3 at the point where x = a. m = (b) Find equations of the tangent lines at the points (1, 4) and (2, 2). y(x) = (at the point (1, 4)) y(x) = (at the point (2, 2)) (c) Graph the curve and both tangents on a common screen. say and the sose m of the target to the survey * 2...
Question 8 a) Find: (3x3 – 5x2 + x - 4) dx (4 marks) b) Use the trapezium rule with 6 strips to approximate the area bounded by the curve y = (x - 1, the x -axis and the lines x = 2 and x = 5 (6 marks)