QUESTION 17 дz If xyz +2 = 15 defines z implicitly as a function of x and y, then дх (2,1,3) 1 ОА 4 Ов —1 о о 3 OD. — 4 OE 3 8
Find the first partial derivatives of the function z = (3х + 8y)1. дz 1. ІІ дх дz. 2 . ІІ ду
Step 2 For F(x, y, 2) = 8exy sin(2) ј+ Зy tan- n (3) k, we have the following. дR - дQ ду дz E др — aR дх дz X X X дQ дх ӘР ду Submit Skip (you cannot come back)
dz Consider the equation 6 sin(x + y) + 2 sin (x +z)+ sin(y +z)= 0. Find the values of and dz ду at the point (41,41,- 3x). dx dz cx (Simplify your answer. Type an exact answer, using radicals as needed.) (41,4x - 3x) dz dy (43,4%, - 3x) (Simplify your answer. Type an exact answer, using radicals as needed.)
4. (a Let (sin( x cos( ) dr + (x cos(x + y) - 2) dy. dz= Show that dz is an exact differential and determine the corresponding function f(x,y) Hence solve the differential equation = z sin( Cos( y) 2 x cos( y) dy 10] (b) Find the solution of the differential equation d2y dy 2 y e dx dæ2 initial conditions th that satisfi 1 (0) [15] and y(0) 0 4. (a Let (sin( x cos( ) dr...
2. Coordinate computation application sin(Az) and y = y\-+ DA cos(AZAR ) Хв — хд +D AE Dropping the subscripts for distance D and Azimuth Az, дх в ду в ду, дХв. Derive: AZ Az. 2. Coordinate computation application sin(Az) and y = y\-+ DA cos(AZAR ) Хв — хд +D AE Dropping the subscripts for distance D and Azimuth Az, дх в ду в ду, дХв. Derive: AZ Az.
3. If z = f(x,y), where x = r cos, y=r sin 0 show that 222 222 1 222 1.az + + +) ar2 ду? ar2 a02 rar
Әf Əf HW: #1. Find the expressions for af of - and om I in terms of адх” ду дz. x = p sino cos 0; y = psin o sin 0; z = pcosø. , where do and of #2. Express V? f in spherical coordinates, where f(0,0,0) is a scalar function.
Verify that the equation is an identity. sin (x-y) tan x- tany sin (x+y) tanx + tany Which of the following statements verifies that the equation is an identity? O A A tan x-tany tanx+ tany sin?(x - y) V1- cos? (x-y) 11 - cos? (x + y) sin(x - y) sin (x+y) O B. sin (x-y) sin cosy - cos x siny sin x- cos y tan x-tany sin (x+y) sin x cos y + cos x siny sin...
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.