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(C) For the function g:R → Z by g(2) = find 9-1({-1,2}). Show transcribed image text
7.) Given f(x,1,2)=x²e (9²2) find: > SPIED A.) x (x, y, z) B.) fy (x,y,z) c.) fz (x,y,z) D.) Syy (x, y, z) 8.) At the Point P (1,2), find the slope of the function $(x,y) = 7x’y in the direction of ū = 43,47
2) (12) f:R-(3/2)-R-10, (x) 1/(3 2x) g:R--21->R-1o), g (x)1/ (x 2) h:R-(-4/3]-R-(1/3), h(x) (f o g) (x) Verify if h(x) is one to one and onto. If it is, find the inverse function of h(x).
2) (12) f:R-(3/2)-R-10, (x) 1/(3 2x) g:R--21->R-1o), g (x)1/ (x 2) h:R-(-4/3]-R-(1/3), h(x) (f o g) (x) Verify if h(x) is one to one and onto. If it is, find the inverse function of h(x).
3. Let fRR' and g:R R2 be given by a) Write down the derivative matrices g'(u) and f(r) and use the chain rule to find the derivative matrix (g fy (x) b) Are the entries of the new function(go f),(x) a linear or nonlinear function of z? mark 3 marks c) How do you understand the statement "(D() is a linear function" in Section 4.1 of the Class Notes?
Problem 17 Find the natural cubic spline through (0,3), (1,2), and (2,1). Show transcribed image text
Problem 2. Suppose that gx, y, 2) is a function with the following properties: -1,2,-4 5, 9(-1,2,-4)-2, 9u(-1,2,-4) -3, and 9.(-1,2,-4) 6 Answer the following questions, and carefully justify all your answers. (a) Estimate the value of g(-0.8,2.1,-4.2). near y (b) In what direction from the point (-1,2, -4) does g decrease the fastest? What is the rate of change in this direction? (c) Which of the following objects exist(s)? Justify your answers, and find an equation for the ones...
3. Show that (a) the function g: R” → R, given by g(x) = ||2||2, is convex. (b) if f : RM → R is convex, then g:R" + R given by g(x) = f(Ax – b) is also convex. A here is an m x n matrix, and b ERM is a vector. You may use any of the results we covered in class (but the definition of convexity may be an easy way to do this, and gives...
Q2. Consider the following transfer function: 2+1 G(Z) = 22 +2 +0.16 (2) 1. Find the controllable form of the system. 2. Find the observable form of the system. 3. Find the modal form of the system. 4. The system is it contrallable?
Find the discrete time unit step response of the system with transfer function G(z) = (z−1)/z(z+1)
(1 point) Find a possible formula for the function graphed below. The z-intercepts are marked with points located at (3,0) and (-6,0). while the y-intercept is marked with a point located at (0,-). The asymptotes are y = :-1,2 = -5, and 2. Give your formula as a reduced rational function f(x) = I help (formulas) 9 y X2 X T-6
5. Show that 9: R - Z defined by g(x) = to AND that h: Z - Z given by h (2 one-to-one. (The "brackets" represent the ceiling function.) 6. Use the formula for the sum of the first n terms of a geometric sequence to write the following as a closed formula: 2.524+1 ke