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4. Given there exists a function h(z) such that 2rº +5 <h(x) <r4 +5 for all...
(4) Suppose that the joint density function of X, Y and Z is given by )<y <<< 1 f(x, y, z) = { otherwise. (a) Find the marginal density fz(z) (b) Find the marginalized density fxy(x, y) 72 (c) Find E (2)
x if x>3 if 2<x<3 if x < 2 Given the following piecewise function: f(x)={-x |-0.5x if it exists. h Find lim f(2+h)-f(2) -0+
9-24 Evaluate the limit, if it exists. 2 - 6x + 5 9. lim 10_lim x² - 4x 3-4 x - 5 why. - 5x4+ 6 -5 2r² + 3xunt 12. lim 1-1 r2 - 2x 13. lim 21,7t + 3 14. lim -182 - 3x - 4 4 + 12 – 16 15 lim 16. lim h 0 (2 + h): - 8 h 1 + 1 - 1 h 17. lim -27 + 8 18. lim h 0
15. For the piecewise function, find the values h(-4), h(0), (5), and h(8). -4x -9, for x < -3 h(x) = 5, for-3x<5 ( x +3, for x 25 16. Determine the symmetries, if any, for the graph of the given relation. 3x + 2 = y2 17. The weight, W, that a horizontal beam can support varies inversely as the length, L, of the beam. Suppose that a 10-m beam can support 1400 Kg. How many kilograms can a...
f(x +h)-f(x) By determining f'(x) = lim h h0 find f'(5) for the given function. f(x) = 6x2 f'(5)=(Simplify your answer.)
please write clearly
2.) Sketch the graph of a function that satisfies all of the given conditions f(0) = f'(4) = 0, f'(x) = 1 if x < -1, f'(x) > 0 if 0 < x < 2, f'(x) < 0 if-1<x<0 or 2 <x< 4 or x > 4, lim f'(x) = 0, lim '(x) = -0, f"(x) > 0 if -1 < x < 2 or 2 <x< 4, f"(x) < 0 if x > 4 1-2
Find indicated quantity if it exists.
La x + 3 if x < -2 54. Let f(x) Find IVx+ 2 if x > -2 (A) lim+ f(x) (B) lim-f(x) (C) lim, f(x) (D) f(-2) x-27
QUESTION 3 Use the graph to find the limit, if it exists. lim f(x) =[a] x + 1 3(x) co . - 2 - -1 -27 QUESTION 4 Use the graph to find the limit, if it exists. 4 lim XO 1 2+ex =[a] 2 - 2 QUESTION 5 Use the graph to find the limit, if it exists. lim tan X = [a] XT/2 Fla T 1
(1) Let G(,y, z) = (x,y, z). Show that there exists no vector field A : R3 -> R3 such that curl(A) Hint: compute its divergence G. (2) Let H R3 -> R3 be given as H(x,y, z) = (1,2,3). Find a vector potential A : R3 -> R3 such that curl(A) smooth function = H. Show that if A is a vector potential for H, then so is A+ Vf, for any f : R5 -> R (3) Let...
2. [10]For the function, f(x), given on the interval 0 <x<L (a)[4] Sketch the graphs of the even extension g(x) and odd extension h(x) of the function of period 2L over three periods (b)[6] Find the Fourier cosine and sine series of f(x) f(x) = 3 - x, 0<x<3