5. The function z(x, y, t) is given by z(x, y, t) Find z and Ztt. = sin (√3+7t2) cos(3x) sin(8y).

Q: Option 2: Problem Solving You wish to invest P10,000 for a period of 5 years. Which of the following…

A: The principal amount we have is ₱10000 and the time period is 5 years.  Therefore,  P=₱10000 t=5

Q: u(x, y) = -e sinx - 2e* siny. Find a harmonic conjugate v of u, namely a function v such that the…

A:

Q: Find the fay and fyy: f(x, y) = xe" - sin(xy) + x³y

A: fx,y=xey-sinxy+x3y

Q: (b) Verify that the following function is harmonic u(x, y) = −e sin x - 2e-siny. Find a harmonic…

A: Here we have to verify that the function is harmonic and then find the harmonic conjugate.

Q: 3. Find , 9 for the functions: ax' ây sin(x³ + y* ) x* +y , (x,y) = (0,0) f (x.y) = .(x.y) = (0,0)

A: f(x,y)=sinx3+y3x2+y2, x,y≠(0,0)0, (x,y)=(0,0)

Q: Find the smallest interval in x over which the functions sin(x/xo) and cos(Tx/xo) are orthogonal. On…

A:

Q: Q1) Verify that the following functions u is harmonic, and find a conjugate harmonic of function…

A:

Q: Find V · (V × F) if F(x, y, z) = sin xi + cos(x – 2y)j + 8zk. | V ·(V × F) :

A:

Q: F. dr Evaluate So

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

Q: 3. If G = (2x²y – x*)î + (e*y + y sin x)j+ (x² cos y)k, find: %3D дхду

A:

Q: The value of sin(2P) + sin(3Q) + sin(4R) at x = 5, y = −3, z = 2, where ▼ × F = (P, Q, R) and F =…

A:

Q: Given f(x, y, z) = 4 sin(x + y), find f, -3 -3 and f. -3 2

A: f(x,y,z)=4sin(x+y) we simply replace value of x , y and z

Q: Find , where : = sin (x²) cos (y) COS 6.x sin (a) cos (y) 2.x sin (a) O2.x cos (2) 2r sin (2*) cos…

A:

Q: Given f(x,y,z) = sin (5xy) + 3xyz3. Find fzzx(5,2,3). %3D zZx Answer:

A:

Q: Let f(z) = 5z2 + 3z.  Find u(x,y) if z = 8.2 + 5.9i

A:

Q: Find a function f such that Vf = 2e²x cos(5y)i - 5e²x sin(5y)j + z³k. f(x, y, z) =

A: Given :-  = 2e2x.cos(5y)i - 5e2xsin(5y) j + z5kNow,

Q: 3. Let f(x, y) = x³ 3x² + xy +7 and u = 0.6i + 0.8j, then find Duf(1,-2).

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: Given f(x, y) = sin(x2) + xy³, find Duf(x, y) where u is in the direction of (1, 2). What is Duf(-2,…

A: To find the directional derivative of given by function

Q: Q11] Using the properties of the FT, calculate the FT of the following functions: (a) x¡(1) = 5 + 3…

A: Let Fourier transform F is defined as Ff(t)=F(ω)=∫-∞∞f(t)e-iωtdt Solution a:…

Q: u(x, y) = -e sin x - 2e* siny. Find a harmonic conjugate v of u, namely a function v such that the…

A:

Q: 4. Determine whether the pairs of functions are linearly independent or linearly dependent on the…

A:

Q: 1. Differentiate. a) f(x) = x43x b) g(x) = x² — e√x -

A: We need to perform differentiation.

Q: Find a function f such that Vf = 2e²x cos(5y)i - 5e²* sin(5y)j + z5k. f(x, y, z) =

A: The given gradient function

Q: 50° S. 80° R 60° 100 7. 7.

A: The measure of the arc length is double than the angle formed by that arc to the circumference of…

Q: Given f(x, y) = sin(x + y) where x = sºt5, y = 6s – 5t. Find

A:

Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

A:

Q: c) Let f(x, y,z) = cos (xyz)sin(x²y=

A: The given function is f(x,y,z)=cos2(xyz)sin(x2y2z2) ..............(1) we have to find;  fx=∂f∂x=?and…