Compute the Jacobian for the substitutions x = ρsinφcosϴ,  y = ρsinφsinϴ,  z = ρcosϴ.

Q: Find əw/ar and aw/as when r = n and s = 0 if w = sin(2x – y), x = r + sin s, y = rs.

A:

Q: of

A:

Q: Find cot β if csc β= -(3 √5)/5 and sec β=-3/2 A) (√5)/2 B) (9 √5)/10 C) (5 √5)/2 D) (2 √5)/5

A:

Q: 2. 2. Let そニと X=UV, y = sin v, Use ナ chain chain Rule to find Ev.

A: 1) The given function z=e2x2y+3xy2 Differentiate with respect to x taking y as constant…

Q: F. dr Evaluate So

A: In this question, we have to evaluate the line integral for given vector function along the given…

Q: (r,1) = (r sin (f), r– cos (1)), (r.1) = (5,-) s numbers in exact form. Use symbolic notation and…

A: In this question, the concept of the Jacobian of functions is applied. The Jacobian of Gr,t is…

Q: Let F = cos(5t) i+ 3tj+ 5t° k and G = ° cos(5t) i +²j+5e* k Find the cross product Fx G =

A:

Q: Calculate for w-z sin(xy+).

A: The given function is w=zsinxy4+9z

Q: Find the cross correlation of functions sin o t and cos Ot

A:

Q: Find sun alpha and tan alpha if the terminal side of alpha lies along the line y=-8x in Q2

A:

Q: Let Compute dw Əs dw Ət -(-3,-4)= -(-3,-4) = w = -5xy + 4yz - xz, x = st, y = est, z = t²

A:

Q: Let Compute θω Əs δω Ət -(-3,-4) (-3,-4)= = w = -5xy + 4yz - xz, x = st, y = est, z = t²

A:

Q: Let X1,..., Xn be i.i.d. Gamma(a, B) with a > 0 and B > 0. Find the MMES of a and В.

A: Let x1, ..., xn be the i.i.d Gamma(α, β) ;α>0, β>0. Find the Method of Moment Estimator of α…

Q: A. Verify Clairaut's Theorem for the given function: F(U,W) = Sin(UW)- 4U?w2 %3!

A:

Q: Find the function f(x) = a + b cos Tx +csin 7x interpolating the data {(0,2), (1/2, 5), (1, 4)}.

A:

Q: Compute the Jacobian at the indicated point. G(r, t) = (r sin (t), r – cos (t)), (r, t) = ( 6,…

A: Jacobian of the function at a given point

Q: Let Compute θω Əs δώ Ət -(-3,-4) -(-3,-4) = w = -5xy + 4yz - xz, x = st, y = est, z = t²

A: By chain rule, we will solve the problem.

Q: ôw ôw + = 0 for w = Ax, y), x = u – v, and y = v – u and demonstrate the ди ду 6. Show that result…

A:

Q: Evaluate ([cos (x – y)sin(x+ y)dA, where R is the triangle with vertices (0,0), R (-1,7), and (7,7)…

A:

Q: Given a function f(x, y, z) = cos (x + xy²z²), find: f#(5,1, 1) = frz (T, 1, 1) = %3D

A:

Q: Find дz ax and дz at (0,0,0) if x3 + z2 + yexz + z cos y = 0. ду

A:

Q: The functions cos r and cos- are linearly dependent (0, ) on

A: evident from the two curves that after zero in a positive direction the two graphs coincide with…

Q: Differentiate

A: Formula:

Q: Let x' = (1, 1, 3) and y' = (-2, 0, -2). calculate the angle between x and y

A:

Q: fex) Cos X ノ

A:

Q: et f(x, у, z) %3 ху + z', Р %3D (3, 9, 1

A:

Q: Use the Chain Rule to find ∂z/∂s and ∂z/∂t. z = tan(u/v), u = 3s + 9t, v = 9s − 3t ∂z ∂s ∂z…

A: Here Z is a function of u and v. u and v are both functions of s and t.So, we can say that Z is a…