
EXERCISE - The equation to the locus of the poles w...t. tox+y = a' tangents to...
Given an equation of a hyperloola w asymptote 3 x-4y=!1, 3x +44 = A) Find the equation of the given hyperbola B Find the center vertices, focci eccentricili
4. Find a rectangular equation for the plane curve defined by the parametric equations x=3sin()y = 3 cos(1) (a) y = x-3 (C) y = 7-9 (b) x + y = 9 (d) x+y = 3 5. Write the equation r = 4 cos in rectangular form. (a) x + y - 4y (b) x² + y = 4x (C) (x + y) = 4x (d) (x+y)* = 4y 6. Write [2(cos 15° + i sin 15°)] in rectangular form....
Exercise 3 Given is the following partial differential equation: Show that w(x, y, z)= sin(52) is a solution of this partial differential equation. Exercise 4 Given is a three-dimensional volume enclosed by the planes y=0,2 = 0, y = and z=a-x+y, with a > 0 a constant. -x (4a) Make a three-dimensional sketch of this volume. Clearly indicate all characteristic features. (4b) Give an integral, with integration boundaries, that can be used for calculating the volume of the object. (4c)...
Consider the differential equation e24 y" – 4y +4y= t> 0. t2 (a) Find T1, T2, roots of the characteristic polynomial of the equation above. 11,12 M (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. yı(t) M y2(t) = M (C) Find the Wronskian of the fundamental solutions you found in part (b). W(t) M (d) Use the fundamental solutions you found in (b) to find functions ui and Usuch...
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6. We say f(x,y) is a function of x +y if f(x,y) = g(x+y) for some one variable function g. For example, sin(a+y) and ex+w' are functions of x + y. (a) Find a condition on the differential equation A(x, y) + B(x,y) = 0 so that it may be transformed into an exact equation via an integrating factor (+ v). (b) What is a formula for this integrating factor. (c) Use this strategy to solve (7x*...
i need help with this differential equations problem
10) Consider the system of DE: x" + 10x – 4y = 0, -4x + y" + 4y = 0 subject to initial conditions, x(0) = 0, x'(0) = 1, y(0) = 0,y'(0) = -1. Denote L{x(t)} = X(s) and L{y(t)} = Y(s). By applying the Laplace transform to each equation, we get the following system a) (s? + 10)X(s) – 4Y(s) = 1, (s? + 4)Y(s) – 4X(s) = -1 b)...
Exercise 1. Tangent plane (15 pts) Let (5) be the surface given by the following equation. x2+y2 = 1+z2 An equation of the tangent plane to (S) at A(1,2,2) is: a. 2x + 4y – 4z = 1 b. x + y - z=0 c. x + 2y – 2z = 1 d. x + y - z = 2 e. None of the above a. b. C. O d. e.
Exercise 5. Extreme values (8 pts+12 pts) Let f(x, y) = 2x2 - 4x + y2 – 4y +1. 1) The number of critical points of f is: a. 0 b. 1 c. 2 d. 3 2) The point (1,2) is: a. a local maximum for f b. a local minimum forf c. a saddle point for f
Exercise 5. Extreme values (8 pts+12 pts) Let f(x,y) = 2x2 - 4x + y2 – 4y +1. 1) The number of critical points of f is: a. 0 b. 1 c. 2 d. 3 mi b. d. 2) The point (1,2) is: a. a local maximum for f b. a local minimum for f c. a saddle point forf b. C.
12 Given the polar equation = determine the kind of conic and the equation of the directrix 4- 3 sin a) Ellipse, y = b) Hyperbola, X= 4 c) Hyperbola, y=- d) Ellipse, y=-4 16