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please write neatly and graph the funtion g. write coordinates and filled in dot or unfilled...
Suppose that the functionſ is defined, for all real numbers, as follows. 3x+1 fx < -2 x-3 if x 2-2 Graph the functionſ. Then determine whether or not the function is continuous. Is the function continuous? 10 X o Yes NO O X ? 2 8 10 -10 Continue
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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
We consider a periodic function of period p = 4 defined by:
Draw the graph of the function to which the Fourier series of the
function g (x) converges on the interval [−6, 6]
x + 2, g(x) -2 < x < 0; 0 < x < 2. 1- x,
UUTUVC vidps O GRAPHS AND FUNCTIONS Evaluating a piecewise-defined function Suppose that the function g is defined, for all real numbers, as follows. =x+2 if x = -2 g(x) = 3 if x = -2 Find g(-5), g(-2), and g(0). 8(-5) = 0 8(-2) = 0 x I ?
Suppose that the function f is defined, for all real numbers, as follows. f(x) = x-2 ifx#2 4 if x=2 Find f(-3), f(2), and f(5). s(-3) = 0 s(2) = 0 r(s) = 1 Suppose that the function g is defined, for all real numbers, as follows. if x -2 8(x)= 1-4 if x=-2 Find g(-5), g(-2), and g(4). $(-5) = 0 DO s(-2) = 1 8(4) = 1
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1. Recall that given a basis, the space of linear endomorphisms of R", End (R"), can be identified with the space of nxn matrices. Let us denote this space by Mat (n). Clearly, with respect to standard addition of matrices and multiplication by scalars, Mat (n) is a na-dimensional vector space. 1. Let X e Mat (n). Then, we can think as being coordinates on Mat (n). 1,j=1...n Clearly, we must...
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8. (a) Find the center of mass of the cylinder {(x, y, z) : x2 +y2 < 1.0 <之-2). given that the density at point (r,y) is ,y, a2 + ). (Observe that 2.2 у = 0 by symmetry, so that no integration is required to find the and coordinates of the center of mass.)
O GRAPHS AND FUNCTIONS Sum, difference, and product of two functions Suppose that the functions,fand g are defined for all real numbers r as follows. 2 g) 2 and evaluate (g n-. Write the expressions for (g-f)(x) and (g+f(r) and evaluate (g.)(-1). (e11)-D
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Given: U(x2)min(3x, ,6x2) P = 4, P-5, 1-20 a) Graph two indifference curves for this utility function. b) Write the function for the budget constraint and graph it c) What are the utility maximizing amounts of x, and x, given the budget constraint? d) Would your answer change if the utility function were U(x1,x2)-min(x,,2%)? Why or why not?
48 The function f is defined by f(x) = for 3 <x< 7. The function g is defined by g(x) = 2x - 4 for .X-1 a<x<b, where a and b are constants. (i) Find the greatest value of a and the least value of b which will permit the formation of the composite function gf. [2] It is now given that the conditions for the formation of gf are satisfied. (ii) Find an expression for gf(x). [1] (iii) Find...