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f(x, y) = sin '() - x?) 8. (6 pts) Find the domain of the following...
1. Sketch the domain of the following functions. (6 Pts) 12+y2 a) f(1,7) (b) g(x, y) = x2 + y2 - 4
q1 Q.1, 2+2 pts] Sketch the domain of the following functions: (a) f(r, y)=Vry 4 25 x2-y-2 (b) f(x,y,z) = V フy Q.1, 2+2 pts] Sketch the domain of the following functions: (a) f(r, y)=Vry 4 25 x2-y-2 (b) f(x,y,z) = V フy
7.(12 pts.) For the function f(x,y)=7 find (a) Domain off. (b)f (6, 10). (c) Find all the second partials fxx fxy, fyx and fyy.
(6 pts) (11) Find the domain and range of the function (x) - 3 - 25 - x (Hint: Graph it.) (4 pts) (12) Suppose that f(x) - (X-4 XS2 X > 2 Evaluate each of the following: (a) f(-5) (b) f(5) (8 pts) (13) If h(x) = 5x73, find h'(x). pts) (14) Find an equation of the parabola with vertex (5. --3) and which passes through the point (2.4)
QUESTION 5 a) Find and sketch the domain of the function f(x,y) = \n(x2 - y +1) + VÝ +1. (5 marks) b) Evaluate eży sin(3x +2y) lim (x,y) (-2,3) 3x +2y (6 marks)
Find the absolute maximum and minimum of the function f(x, y) -ry1 on the domain D (r, y),y 20, x2 +y2< 1) rty+1 Find the absolute maximum and minimum of the function f(x, y) -ry1 on the domain D (r, y),y 20, x2 +y2
... Find the domain of the function f(x, y) = ln (2 - y2). A) All points on or to the left of 1 = ya B) All points on or to the right of x = y2 C) All points to the left of x = y2 D) All points to the right of x = y2 E) All points on or to the left of 2 = 0
sin 3x 8. Find the first four nonzero terms in the Maclaurin series for f(x) = х 1 1 1 sin x = x - --- 203 + -25 120 X' +.. 5040 (14 pts.) 6
Q1. Let z = f(x,y) -√4x² – 2y² Find (i). domain of f(x,y) (ii). range of f(x,y) (iii). f(1,1) (iv). The level curves of f(x,y) for k = 0,1,2 4x2y Q3. Let f(x,y) = x2+y2 if (x,y) = (0,0) 1 if (x,y) = (0,0) Find (i) lim limf(x,y) (x,y)-(0,0) (ii). Is f(x, y) continuous at (0,0)? (iii). Find the largest set S on which f(x,y) is continuous.
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y = f'(x) (c) state the domain of f and the domain of f. Find lin tan 4x cos 3x sin 5x X> 12 Find y if y = (3x+5)*(x+4x) (3 Find y' it ya + 10x tanx 7 Let y= (a) Find (6) Find the equation of the tangent line at (74 y' Elf 8 X3 Prove lim (5-) = 4 (a) write the...