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Question how to do those? src="/qa/attachment/10702685/" alt="20191002_195300.jpg" /> Attachment 1 Attachment 2 Attachment 3 ATTACHMENT PREVIEW Download attachment 20191002_195300.jpg 7:51 1 0 &amp; vy ON all 79% H14pt3.pdf . . Math 2415 Homework on 14.3 1. Compute the partial derivatives of, of, off, at, and andy of the following functions. (a) f(x,y) = x cos x sin y (b) f(x,y) = e-(22+y?)/(202) 2. Let f(p, 0, ) = psin ocos 0. Calculate of and of 3. The plane y = 2 intersects the graph of z = ry3 +5x2 in a curve. Find a parametrization of the tangent line to this curve at the point where x = 3. df 6. nbraries/ MW .pdf 7. Verify that the function u(x, y, z) = log (x2 + y?) is a solution of the two dimensional Laplace equation uxx + Wyy = 0 everywhere, except of course at the origin where f is not defined. 8. Verify that the following functions solve the wave equation, Utt = Uzz (a) u(x, t) = cos(4x) cos(4t) (b) u(x, t) = f(x -t) + f(x+t), where f is any differentiable function of one variable. O ATTACHMENT PREVIEW Download attachment 20191002_195337.jpg 7:51 6 H C“ at.- El i i i 8 H14pt4.pdf Math 2415 Homework on 14.4 1. Find an equation for the tangent plane to the surface 2 = My 7 1‘ at the point. (as, y, z) = (1, 2, 1). 2. Let f(1‘,y) : 123,12 7 1'. {3] Find the equation for the tangent plane to the graph of f at (2. l. 2). (b) Use a linear approximation to ﬁnd the approximate value of f(1.9, 1.1). 3. Calculate the linearization of the function f at the point P and use it to estimate f (Q) for {a} z : ﬁshy) : [1r — y) cos(21rsry) where P : (1%) and Q : {1.1.0.4} . P 6. The period of oscillation of a pendulum of length L is given by the formula T : 27r L/g. Where g is the acceleration due to gravity. Estimate the change in the period of the pendulum if its length is increased from L = 30 cm to L = 3] cm and it is simultaneously moved from a location where g = 9.8 m/s2 to one where g = 9.85 m/sz. III C) &lt; ATTACHMENT PREVIEW Download attachment Screenshot_20191002-195059_Drive.jpg 7:50 1 0 &amp; v Call 79% H14pt1.pdf . . Math 2415 Homework on 14.1 1. Stewart 14.1.44 2. Sketch the level curves f (x, y) = c of the following functions z = f(x, y) at the specified values of c. Then sketch the graph of f. (a) f(x, y) = (100 - x2 - 72)1/2, c = 0, 2, 4, 6, 8 (b) f(x, y) = y - x2, c=0, +1, +2. 3. Sketch the level surfaces f(x, y, z) = c of the following functions w = f(x, y, z) at the specified values of c. (a) f(x, y, z) = 4x2 + 2 + 922, c = 0, 1, 2. 4. Match the functions z = f(x, y) with the surfaces representing their graphs. Justify your answers. (The origin is in the middle of each box. The figures only show that portion of the surface that is inside a box.) (a) f(x, y) = x2+2 (b) f(x,y) = (x2 - y?) exp(-12 - y?) (c) f(x, y) = sin(x2 + 2y?) III IV V VI VII VIII IX X 1 O

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