If we discuss the derivative of the function f(z) = z. Imz by Cauchy- Riemann equations. we see fz) can not be differentiable at any polnt in the Z- plane FO TO

Q: ) Find symmetric equations for the tangent line to the graph of f(r, y) = at (1, 2, 2) in the plane…

A:

Q: In explicit method of hyperbolic PDES, the second initial condition, the one involving g, gives…

A: Given,

Q: Prove the formula for the derivative of a) (Inverse of cotangent) b) (Hyperbolic cosecant) y = csch…

A: formula for derivative of both function is following:-

Q: 2. Find the coordinate of the points on the cardioid r=1- cose at which there is a horizontal…

A: We are given the polar curve: r = 1- cosθ use formula:         x=r cosθy=r sinθ then,  dxdθ=-sinθ+2…

Q: 6. Where does the tangent line to r = at the point (1, 0, 1) intersect the y-z plane.

A: Given:

Q: By using caushy Rieman find the derivative of f(z) =|z| if it exit

A:

Q: Find the slope of the tangent line to the curve of intersection of graph of f and the plane x =2 at…

A:

Q: Find an equation of the tangent line to the astroid at the (3√3, 1).   x2/3 + y2/3 = 4

A: Given an astroid equation find the equation of tangent at a point.

Q: Find the equation of the tangent plane to z = In(x?y) – x/ỹ at (-,4). %3D

A:

Q: Is there a smooth (continuously differentiable) curve y f(x) whose length over the interval 0sxsa is…

A:

Q: A Bifolium is the family of curves given by (x +y)* = kx²y, where k is a real number constant. %3D…

A:

Q: Find the derivative of f (z) = (2° – 5z) (2² + 6z – 6). a va la sin (a) f' (포) 3DD Please explain,…

A:

Q: ) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

A:

Q: Find the point where the CAUCHY- RIEMANN equation is satisied for the function f(2) =xy+Xyi

A:

Q: Find the equation of the tangent plane to z at (-4,2).

A:

Q: Find the derivative dydx of the hyperbolic spiral r=aθ.

A:

Q: prove that the curve y = f(x),(Ax) >0) and y = (x)sin x ,where fx) is differentiable function ,have…

A: We use the Given Curves, Prove that have a common tangent at common point.

Q: 5. Find the equation of the tangent plane of sin(xyz) = x + 2 y + 3z at the point (2, -1, 0).

A: We have given the surface X,Y,Z at the point (2,-1,0). We have to find the equation of the tangent…

Q: Find an equation for the tangent plane to z-x-y = 3 at the point (2, 1, 8) Z - ) %3D

A: given z-x2-y2=3 at point 2,1,8

Q: Construct a cubic spline that interpolates sin x at nodes 0, T/2, T, 37/2, 27 (use the true…

A: The given function is fx=sinx and the given node points are x=0,π2,π,3π2,2π. Therefore the given…

Q: Prove the below function is not analytic at z = 0, By calculating all the directional derivatives of…

A: Consider the given function, fz=z2z:z>00:z=0 Let z=x+iy, then we can write the function as,…

Q: The tangent function is integrable from 0 to T. True False

A:

Q: 2. Determine the directional derivative for u = log, x2lnz if it is defined by the direction at dx =…

A: Given u=logyx2lnzby the direction at dx=dz, dydx=2and is situated at a point in the Euclidean space…

Q: Use Caushy Reman equations to Show that ĕ (Z) anel its derivative f(Z) exist Verywhere and find ぐ(z)…

A: Given: fz=z3 Rewriting given function we get, fz=x+iy3fz=x3-3xy2+i3x2y-y3 Now comparing, it with…

Q: Find the tangent line to f(x) = ax³ at x = -1. Assume that a is a positive constant. ***

A:

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

A:

Q: Find the equation of the tangent line to the curvef (x) = -x' + 2x at x = 1. о Тx) 3D 1 + (-1)(х —…

A: To find the equation of tangent line to the curve at x=1

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

A: we have to derivative

Q: 7) Use a tangent line approximation with the function g(x)= Jx to estimate 9.2 . %3D

A: topic - tangent line approximation note :as per bartleby guidelines we are supposed to answer only…

Q: Find the equation – in any convenient form – of the tangent plane to z = x² sin(x+2y) at the point…

A:

Q: By using caushy Rieman find the derivative of f(z) =|z| if it exit O fiz) = 2 +I21

A: As per bartleby guidelines only 1 question can be answered please upload the questions separately.…

Q: 8. Find a parameterization of the tangent line to r(t) = (cos(t), sin(2t)) at the point

A:

Q: Let z = x+iy and f(2)=√√|xy|. Show that ƒ(z) satisfies the Cauchy-Riemann equations at the origin,…

A:

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: Find the tangent line to the graph the eq uati on of of YCK)- %3D at X=0 11-x2

A:

Q: By using caushy Rieman find the derivative of f(z) =Iz| if it exit ® fLz) = 2 +Z1

A: It is given that the function fz=z. The function fz=x2+y2. Note that, If the function is…

Q: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

A: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

Q: Verify the statement by showing that the derivative of the right side is equal to the integrand on…

A: NOTE: Refresh your page if you can't see any equations. . on the right-hand side, we have

Q: 7) Use a tangent line approximation with the function g(x)= Jx to estimate V9.2

A:

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

A: It is partial derivative problem

Q: 2. Find atax

A: The symbol ∂2v∂t∂x is the symbol of partial differentiation. Differentiate the given function v…

Q: Find the fourth derivative of f (z) = 57 + In (z) – 109z. Enclose arguments of functions in…

A:

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

A:

Q: 10. Find a tangent plane to z² – x² +y² = 1 at (7, –5, 5).

A: To find a tangent plane to the given curve at the point (7,-5,5)

Q: nal derivative of ƒ at the given point in the direction indi f(х, у) —D sin(x + 2y), (4, —2), ө —…

A:

Q: Consider the function g defined by 1 g(x, y) = cos (Ta VT)+ log3(x - y) Do as indicated. In what…

A:

Q: the Prove function is analytic at z = 0. By calculating all the directional derivatives of the that…

A: The given function is ; f(z) = z¯2z,if z>00,if z=0 We have to show that the function f(z) is not…

Q: Show that the function f(z)=sin x coshy+I cosx sinh y  is continuous as well as analytic every where

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.