(a) Calculate the line integral of F =r°yi + y°j + z²k along the straight line path from (1, 1,0) to (4, –2,0). (b) Calculate the line integral of F from (1, 1,0) to (4, –2,0) but along the path y = (-2+6)/5, z = 0

Q: Q2) a) Find Maclaurin expression of f (x) = Cosh (x) b)Find the gradient of the function f(x, y, z)…

A: Part (a) General form of function fx is Maclaurin series is…

Q: b) Consider the second-order truncation error (0 (Ax)2) with the step size (-Ax) and then, obtain a…

A: The truncation error is O∆x2 and the step size is -∆x

Q: Let  f(x, y) = sin(15x2 + 3y2) Calculate the quadratic approximation of f at the point (0,0)

A: Given that,  fx, y=sin15x2+3y2 The quadratic approximation of the function fx, y at the point x0, y0…

Q: Get the derivative of the function. Write the final answer in x+jy form 22-9 22 + 1 20z j20y…

A:

Q: 8. Find directional derivative of function z = xey at point P(1,0) in the direction from pointP(1,0)…

A:

Q: 2.10. Orthogonally diagonalize the rotation matrix - sin a Cos a sin a Ro = COs a where a is not a…

A: Rα=cos α   -sin αsin α       cos αTo find the eigen value of Rαlet (R-λI)=0cos α-λ-sin αsin αcos…

Q: Find the number of zeros of f(z) = z' + iz² – z + 2i in the upper half-plane.

A:

Q: find the first and the second derivative of these equation , first as a function of z then as a…

A: Given: Since you have asked multiple question, we will solve the first question for you. If youwant…

Q: d) Consider the fourth-order truncation error (0(Ax )4) with the step size Ax and also (-Ax) then,…

A:

Q: Calculate the directional derivative of y = xz + y? in the direction of 20 – ŷ + 32 at the point (2,…

A: Given that ψ=xz+y2and the direction vector2x⏞ -y⏞+3z⏞The point p0=(2,0,-1) To find the directional…

Q: Plot the slope field of y=x+y using slopes m = -3, -2,-1,0, 1, 2. Sketch integral curves for…

A: First we plot the slope field and then plot the curve .

Q: he surface al derivative

A:

Q: Find the tangential and normal components.  r(t)=(t+1)i+2tj+t^ 2 × k     ,   t = 1

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Find the derivative of the function f (, y, z) = 4ay z at the point (4, 64, 16) in the direction of…

A:

Q: Find the approximation for the Green's function of the one-dimensional acoustic wave equation in the…

A: Given function is, cx=aebx Here, a>0 and it's constant here we have to see the effect of b so,…

Q: Compute F · dr where F(x, y) = and C is the path traced by the line segment starting at (0, −1) and…

A:

Q: bee with a velocity vector r' (t) starts out at (7, -3, 7) at t = 0 and flies around for 6 sec me t…

A: We know position vector of bee if it has a velocity vector  is We are given

Q: Consider (x, y, z) = 4xy²+ 3y sin(z) and at the point P = (1,2,0) calculate the directions in which…

A: Approach to solving the question:To find the directions in which the…

Q: Suppose F(x, y) = −y sin(x)i + cos(x)}. (a) Find a vector parametric equation for the parabola y =…

A:

Q: 3. Find the derivative of the function f(r, y, ) = xy + yz+ the direction A = 3i + 6j – 2k. zr at…

A:

Q: Find all residues of the function z (2-2) not including the residue at infinity. "

A:

Q: 4) Find the total derivative of the function: a.f(x, y) = ex²+y² 1 c. T(l,g) = 2₁ 2TT. b. z = x siny…

A: Total derivative of a function f(x,y) is given by df=fx dx+fy dywhere fx=∂f∂xfy=∂f∂y