Find the following trigonometric limit: lim sin - Hint the substitution [((u-1)E)s01 u= t-n makes life...
number 4 1. Find the limit of the following sequences (find lim an) n n a.) an = n +3 b.) an = V35n n- 2. Determine whether the following series converge or diverge. -3 (n + 2)n + 5 b.) tan-'(n) n2 + 1 a.) 5 nel 3. Determine the radius of convergence and the interval of convergence of the series 2" (x – 3)" n n=1 n=0 (-1)", 2n 4. Using the power series cos(x) (2n)! (-« <...
5. Imagine a string that is fixed at both ends (e.g. a guitar string). When plucked, the string forms a standing wave. The vertical displacement u of the string varies with position r and time t. Suppose u(x,t) = 2 sin(nx) sin(mt/2), for 0 x 1 and t 0. Convince yourself of the following: If we freeze the string in time, it will form a sine curve. Alternatively, if we instead focus on a single position, we will see the...
u=2i-j+k v = 37 - 4k w = -51 +7 QUESTION 1)Find the volume of the parallel face determined by the vectors QUESTION 2) f(x, y, z) = xy + y2 + zx a) Find the gradient vector of function f b) Calculate the gradient vector at point P (1, -1, 2) of function f. c) Direction in the direction of the vector v = 3i + 6j - 2k at point P (1,-1,2) of the function f find the...
Problem 1. Consider the nonhomogeneous heat equation for u,t) ut = uzz + sin(2x), 0<x<π, t>0 subject to the nonhomogeneous boundary conditions u(0, t) t > 0 u(n, t) = 0, 1, - and the initial condition Lee) Find the solution u(z, t) by completing each of the following steps: (a) Find the equilibrium temperature distribution ue(x). (b) Denote v(x, t) u(a, t) - e(). Derive the IBVP for the function v(x,t). (c) Find v(x, t) (d) Find u(, t)...
Problem 1. Consider the nonhomogencous heat equation for u(a,t) subject to the nonhomogeneous boundary conditions u(0,t1, t)- 0, and the initial condition 1--+ sin(z) u(z,0) = e solution u(z, t) by completing each of the following steps Find the equilibrium temperature distribution we r) Find th (b) Denote v, t)t) - ()Derive the IBVP for the function vz,t). (c) Find v(x, t) (d) Find u(x, t) Problem 1. Consider the nonhomogencous heat equation for u(a,t) subject to the nonhomogeneous boundary...
Provide an appropriate response. Find the second derivative of the the function y-sin-12x och 1 - 4x2 2(1 - 4x2,32 (1 - 4x2,312 "-4392 Find any 5**v = yn In 5 In y 5x + y -5x + y + in 5-1 5x + y 5x + V + In 5 vin 5 - 1 vin 5-1 Find the derivative of y with respect to x, t, or, as appropriate.y = 4+2ee dee Use l'Hopital's Rule to evaluate the limit....
Whats the answer to number 1? 1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j + ick)...
what is the answer for number 4 1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j +...
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
Find magnitude of velocity and acceleration at t=1 Part A Learning Goal To be able to calculate position, velocity, and acceleration of an object in curvilinear motion using a rectangular coordinate system. A car drives on a curved road that goes down a hill. The car's position is defined by the position vector An object's motion can be described along a path represented by a fixed x, y, z coordinate system. In such a system, the position vector, r, is...