If z = x + jy, then O Check whether the function f(z) : 1 is an entire function. State the reasons. 1+|z|? (ii) Show that lez*+j) + e¬jz²| < ev³–3x²y + e2xy

Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

Q: 75. F(x) : (t + 2) dt

A:

Q: Find the direction at which the function f(x, y, 2) = a In(e-az) increases fastest at (-3,0, 0) O…

A:

Q: Value of divergence of function (x2y2)î - (z³y 4x) ĵ + 4y² xk at (1, 2, 1) is

A: Given vector is (x2y2)i^ - (z3y-4x)j^ + 4y2xk^

Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

A: The given function is g(x,y)=lnx2+y23 We have to find the gradient of the function and maximum value…

Q: What is frz, fyy, and fyz of f(x, y) = In(y²")?

A: Given:           f(x,y)=lnyx2          fx=∂∂xlnyx2         Treating y as constant variable…

Q: Find the linearization at x = a. IT f(x) = sin³ (x), a = 4

A: Given,            The linearization at x=a.             fx=sin3x, a=π4We know that,             The…

Q: Find f-(x, y) and fy(x, y). f(z, y) = (y° tan(5z)) f-(x, y) fy(x, y) =

A:

Q: Find the derivative of the function at P, in the direction of A 1) f(x, y) = 2xy – 3y², P,(5,5), A=…

A: We have given function, we have to find directional derivative.

Q: (b) A bounded, 3B > 0 such that |f(x)| < B Vx € (0,1), continuous function on (0,1) with unbounded…

A:

Q: Find the derivative of the function at P, in the direction of A 1) f(x, y) = 2xy – 3y², P,(5,5), A=…

A:

Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy² = 2 (C- cos x) O…

A:

Q: x2 f (x) = t² sin(2t) dt 1

A:

Q: Find the linear approximation of the function at the given point. f(x, y) = 4 sinx - 6 cos y at (0,-

A: Given,           The function fx,y=4sinx-6cosy  at  0,π2.

Q: Find the linearization of z = f(x,y) at P(-3, 2) when f(-3, 2) = 2 and f-(-3, 2) = 1, fy(-3, 2) =…

A:

Q: Choose the gradient of the function f defined by f(x, y, z)= In[1 + (17xy + xz +9yz)²].…

A:

Q: Use the linearization L(3,-2) (x, y) of f(x, y) = -x²y-xy² near the point (3, -2) to approximate the…

A:

Q: Show that the function x² – y² 2ху f(x,y) = { x² + y² if (x,y)# 0 if (x,y) = 0 is continuous at…

A:

Q: x+y are functions of t.Ue %3D Ronphicit differentiation to express in terms af dx X and y dy

A: Explanation of the solution is given below....

Q: Show that the function defined by xy √x²+y² f(x, y) {{ = 0 if (x, y) = (0,0) is not differentiable…

A:

Q: Consider the function g defined by 1 g(x, y) = cos (Tx /y) + log3 (r y) In what direction does g…

A:

Q: Give 1 problem of partial differentiation of function of U with respect to 3 independent variables…

A:

Q: f(x,y)=ln(5x+4y). Find the directional derivative of f at (1,0) in the direction of the line…

A:

Q: Assuming y cos (3xz) = 5 defines z as a function of x and y. Differentiate

A: we have to derivative

Q: 1. Find the directional derivative of the scalar function f = yzx^2 + 4xz^2 at the point P(1,-2,-1)…

A:

Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy²= 2 (C- cos x) O y…

A: This question is related to differential equations, we will solve it using given information.

Q: dz Use implicit differentiation to find 3x2 1+2y 33y+z x+2yz 323y 1+2y %3D 1+2y

A:

Q: I. Show that the function ƒ defined by (1, y) = (1, –1) f(1, v) = { +g (z, y) # (1, –1) + y is not…

A: We will use the sequential characterization of continuity to solve this problem. The detailed…

Q: Verify Cauchy-Riemann equation for the function f(z) = z^3

A: To find- Verify Cauchy-Riemann equation for the function fz = z3         Formula Used-…

Q: Show that the function f(z) = sin x cosh y + i cos x sinh y is continuous as well as analytic every…

A:

Q: In what directjon from the point ( 1, 3, 2 ) is the directional derivative of 6 = 2 xz-y a maximum ?…

A:

Q: Suppose that f(z, y) = z*y°. The directional derivative of f(1, y) in the directional ( – 1, – 2)…

A: We can solve this as follows:

Q: 23-4z2-2一4 y = %3D 1+ Va

A:

Q: The concept of the linear approximation builds from the fact that differentiable functions are…

A:

Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

A: The solution is given as

Q: Find the linearization of ƒ(x) = sqrt(1 + x) + sin x - 0.5 at x = 0

A:

Q: Find f'(x)'f f (x)= arctan (Inx) %3D

A: Using composite function formula.

Q: Give one problem for  partial differentiation of function of U with respect to 3 independent…

A: It is partial derivative problem

Q: Show that the function f(z)=sin x cosh y+i cosx sinh y is continious as well as analytic every…

A:

Q: Show that the function f(x, y) = 3x - 4y² is differentiable at point (−1, 2)

A: answer is in next step. please give a like !!!

Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: See the attachment

Q: /alue of divergence of function (x2y2)î - (z³y – 4x) ĵ + 4y2 xk at (1, 2, 1) is

A: Let f = (x2y2)i^ - (z3y-4x)j^ + 4y2xk^

Q: Find the direotional derivative of the scalar function f-x'+ y' +2z', at the given point (1,1,2), in…

A: Explanation of the answer is as follows

Q: 12. Differentiate the function (use chain rule): y = 2x2 Vx+1'

A: To differentiate the given function

Q: Calculate fz(2, 3, 1), where f(x, y, z) = xyz.

A: Given,          fx,y,z=xyz

Q: Find the maximum directional derivative of the function f(x.y) = x In y + x2y2 at the point (-1,1).…

A:

Q: Let f(x,y) = x^2 y + e^xy sin y.   At Point (1,0) State the direction where the function…

A: Given: fx,y=x2y+exysiny

Q: What is the maximum value of the directional derivative of f(x, t) = f (x, t) = x² + t²/8 – 10 at…

A: Note: The directional derivative of a function is the rate at which the function changes at a…