using the general power rule Question 1 let y = (x2 +x)3 Find y' 2x+1 3(x2+x)2 3(x2+x)2 (2x+1) • (x2+x)2 (2x+1) recall general power rule formula has three parts: [u(x)" ]' = n u(x)" 1 u'(x) Question 2 let y = (x3 +x2) 1/3 Find y' (x3 +x2) 1/3 (1/3) (x3 +x2) 1/3 . (1/3)(x3 +x2)-2/3 (1/3)(x3 +x2-2/3 (3x2+2x) recall general power rule has three parts. [u(x)"l' = n u(x)n-1 u'(x) Question 5 let g(x) = 1/(x3+x2)3 find g'(x) (x²+x23...
5. Use Scilab to create following rational expression matrix: 12x 2 1+x 1x2 1 x2 1 +x 3 x 1+x3x3 5x x3 2 x2 1 x3 6 1+2x 1+ 3х + x2 1-х+x2. 5. Use Scilab to create following rational expression matrix: 12x 2 1+x 1x2 1 x2 1 +x 3 x 1+x3x3 5x x3 2 x2 1 x3 6 1+2x 1+ 3х + x2 1-х+x2.
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
16. xyty Let f(x, y) = x3 + xy + y}, g(x, y) = x3 a. Show that there is a unique point P= (a,b) on 9(x,y) = 1 where fp = 1V9p for some scalar 1. b. Refer to Figure 13 to determine whether $ (P) is a local minimum or a local maximum of f subject to the constraint. c. Does Figure 13 suggest that f(P) is a global extremum subject to the constraint? 2 0 -3 -2...
4.) Let X1, X2 and X3 be independent uniform random variables on [0,1]. Write Y = X1 + X, and Z X2 + X3 a.) Compute E[X, X,X3]. (5 points) b.) Compute Var(x1). (5 points) c.) Compute and draw a graph of the density function fy (15 points)
Determine whether the system is consistent 1) x1 + x2 + x3 = 7 X1 - X2 + 2x3 = 7 5x1 + x2 + x3 = 11 A) No B) Yes Determine whether the matrix is in echelon form, reduced echelon form, or neither. [ 1 2 5 -7] 2) 0 1 -4 9 100 1 2 A) Reduced echelon form B) Echelon form C) Neither [1 0 -3 -51 300 1-3 4 0 0 0 0 LOO 0...
Let x = [X1 X2 X3], and let T:R3 → R3 be the linear transformation defined by x1 + 5x2 – x3 T(x) - X2 x1 + 2x3 Let B be the standard basis for R3 and let B' = {V1, V2, V3}, where 4 4. ---- 4 and v3 -- 4 Find the matrix of T with respect to the basis B, and then use Theorem 8.5.2 to compute the matrix of T with respect to the basis B”....
do 11.3 please Example 11.2b Let us reconsider Example 11.2a, where we have 5 to invest among three projects whose return functions are f(x) = 2x . 1+x f(x) = 10( I-e-x). Let xi (j) denote the optimal amount to invest in project 1 when we have maxlfi(l), f2(1), f3(1))-max(5, 1632 6.32, a total of j to invest. Because we see that Xi(1)=0, X2(I) = 0, x3(1)=1. Since max(f(xdl) + I)-f(xdl)) = max(5, I, 8.65-6.32) = 5. we have X1(2)...
; Let at be a linear transformation as follows : T{x1,x2,x3,x4,x5} = {{x1-x3+2x2x5},{x2-x3+2x5},{x1+x2-2x3+x4+2x5},{2x2-2x3+x4+2x5}] a.) find the standard matrix representation A of T b.) find the basis of Col(A) c.) find a basis of Null(A) d.) is T 1-1? Is T onto?
10r y Which ofthe flywing is equivalent 1T77 ? 2x A. 9. B. 2y 2x 3r -9x + 18 10 Which of the following is equivalent to the fraction 6-x x2-25 When is divided by , the quotient is x +5 9x A. 27x B. 3r-15 x-20 C. 12. Which ofthe following is equivalent to-li A. B.一 D. 13. Which equation represents a line that is perpendicular to the line represented by 2x-y 77 B. y=-x+6 C. y=-2x + 6...