2r2-3ry equation for the tangent plane to the graph of f(x, y) (2, 1). 5. Find an at (r, y) 2r2-3ry equation for the tangent plane to the graph of f(x, y) (2, 1). 5. Find an at (r, y)
Set up a function can be written as: (si = if) (a) Solve exactly the recurrence when n is the power of 2, using the method of the characteristic equation and show your steps. (Start by asking n = 2k.) (b) Explain how to derive the exact order of T (n), i.e., Θ (T (n)), expressed simply. si n 1 si n 2 77 (n/2]) — 10Т(n/4]) — %п si п > 2. 1 T(п) —D { 8 si n...
Use equation (5.13) and the Fourier integral representation of to write a solution of the problem on the real line: Also reformulate the solution using equation (5.18). Problem: Equation (5.13): Equation (5.18): f(r kurr for x<, t> 0 ut u(x,0) f(r) for 7 for r> f (z)sin 0 u(x, 0) acos(wr)sin (wr)]e-ktdu u(, t) 2 T kt f()e (-)2/4ktds
Problem 3: (5pts)Prove that the following equation has at least one solution: sin x Problem 2: (10pts) Find horizontal and vertical asymptotes of f6 2+16+64 2r2 +11-21 Problem 3: (5pts)Prove that the following equation has at least one solution: sin x Problem 2: (10pts) Find horizontal and vertical asymptotes of f6 2+16+64 2r2 +11-21
1. Given y” + 3y' - 2y 0. Give the characteristic equation (the quadratic equation that finds the roots). (a) r2+ 3r - 2 = 0 (b) r2+ 3r + 2 = 0 (c) 2r2+ 3r - 1 = 0 (d) 2r2+ 3r + 1 = 0 (e) r2+r-2 = 0 (f) r2+r+ 2 = 0 (g) 2r2 +r-1=0 (h) 2r2+r+ 1 = 0 2. Find the larger root of the auxiliary equation of the differential equation y” + 3y...
2. Consider the surface -v 9-2r2-r : f(x, y) z (a) What is the domain and range of f? (b) Sketch the level curves for 2-f(r,y) -0,-3,-2V2,-v5 (c) Sketch the cross sections of the surface in the r-2 plane and in the y-z plane (d) Find any z, y and z intercepts Use the above information to identify and sketch the surface. 2. Consider the surface -v 9-2r2-r : f(x, y) z (a) What is the domain and range of...
A circular loop of wire having a radius of 5.13 cm carries a current of 0.233 A. A vector of unit length and parallel to the dipole moment of the loop is given by 0.60 i - 0.80 i. If the loop is located in a uniform magnetic field given by B = (0.990 T)/+ (0.626 T) , find (a) the x-component, (b) the y-component, and (c) the z-component of the torque on the loop and (d) the magnetic potential...
Question 2 (3 marks) Function f(t) is described as a sudden change of 1 SI unit at t-0 followed by a sudden change of -1 SI unit after 0.2 seconds. Assume f(t)-0 for t<0. (a) Write the analytical form of f(t). Sketch its graph indicating clearly all relevant values. (b) Find the Laplace transform of f(t) (c) Derive the expression for F, (s) if f(t) f(t)dt (d) Please see over Question 2 (3 marks) Function f(t) is described as a...
9.6 Consider the ideal dc-to-ac inverter shown in Fig. P9.6. Assume Si/S4 and S2/S3 are switched alternatively at a 50% duty cycle with a switch period of T. Let the output current be given by , (t) , sin at, where ω 2π/T. (a) Derive the expression for the instantaneous power delivered to the load. (b) Determine the average power delivered to the load. (c) Discuss the requirement for a practical switch implementation for si- (d) Repeat part (c) for...
3) Let a -pip?.. .Pk and blp22.. .P%* where pi are distinct positive primes and ri, si are non-negative integers. Then show that where for each i, ni minfri, si) (Recall that min{c, d\ denotes the minimum of c and d.) 3) Let a -pip?.. .Pk and blp22.. .P%* where pi are distinct positive primes and ri, si are non-negative integers. Then show that where for each i, ni minfri, si) (Recall that min{c, d\ denotes the minimum of c...