Given, u=x3-y3. Which of the following is correct ? Not harmonic Not analytic Analytic Harmonic

Q: With the aid of residues, and a carefully chosen contour, show that d.x x5 +1 5 sin(T/5)

A: We we solve the general form of the integral for n instead of 5 Then we will substitute n=5 in order…

Q: Use symmetry to evaluate the followingintegrals.

A:

Q: The slope of the tangent line to the graph of f(z) COS at a is Select one: O a. 00 2 Ob. 2

A: we hav eto find the slope of the tangent line of the given graph at a=π/2

Q: Erampole: Are the following Punthien harmonic? If your auswer is y tind a Corresponding ana'ytie-…

A:

Q: Find the tangent of ZZ. 37 35 12 Y Write your answer as an integer or as a decima tan (Z) = Submit

A:

Q: What curves are represented by the following? Sketch them. [cos t, sin 2t, 0]

A: To Sketch: The curves represented by the parametric form [cos t, sin2t, 0].

Q: Find the length of the curve over the given interval. r = 8(1 + cos θ), [0, π/ 3]

A: Given: To find:  The length of the curve over the given interval.

Q: the pont find on tne araph where the tangent Tine is norizontal Of fu) = 30yd-20x-3

A:

Q: Given that Sinh Ys 2. fnd sech x, eanh y with draw atiangle

A:

Q: Q4) The standard formula for the tangent of the sum of two angles is tan x + tan y tan(x +y) 1- tan…

A:

Q: Find the arc length of the following curve on the given interval. x- 24t+9, y= 10t-7,0sts1 The…

A:

Q: Given f(x, y) = 6e sin(2y) %3D Question Help: OVideo

A: We need to find del function at given points.

Q: Which of the following gives the arc length of the parabola 2y = x² - 13xS1 Hint: Use Trigonometric…

A:

Q: 20. Find given that a) y = arctan ) simplifying your answer as much as possible, b) y = In(x'-3x? +…

A:

Q: has at least one solu Prove that the equation r+ sin(x) = VI +3 %3D (0, т).

A: Here we have to prove that,  x+sinx=1x+3⇒f(x)=1x+3-x-sinx has at least one solution in the interval…

Q: Find the tangent of ZD. 3/3 2V10 E Write your answer in simplified, rationalized form. Do not round.…

A:

Q: Find the length of the curve r= 1+ sin(20) Oses- /20

A:

Q: find the length of the part of the r=2(1+ cosa) curve that remaîns în the r =211+ Sind) curve %3D…

A: We have to find the length of the part of the r = 2(1+cos alpha) curve that remains in the r =…

Q: 2. Vy+1-2 dy

A: ∫vn dv = vn+1n+1+C

Q: dz az Find and of the equation z = xy arctan ax ду

A:

Q: Which of the following four fundamental funtions have the same tangent line at x = 0…

A:

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: The given question is the application of integration and solved as shown in step2.

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A:

Q: Select the definitions of sinhx, tanh a, and sech z. O e +e- e -e-z O e-e e +e-z O e -e e +e- O e +e…

A: The hyperbolic function of sine is expressed as-     sinh x=ex-e-x2 Thus, Option (C) is the correct…

Q: Find the area inside the oval limaçon r = 6 + sin 0.

A:

Q: Find the arc length of the following curve on the given interval. x= 213, y = 312, 0sts 3 The arc…

A: Answer and explanation is given below..

Q: Consider the following. x = sinh(t), y = cosh(t) (a) Eliminate the parameter to find a Cartesian…

A: Solution: The objective is to eliminate the parameter to find a Cartesian equation of the curve

Q: Calculate the length of the curve r=a*sin(^3)(x/3) for (x(1)=0, x(2)=3pi)

A:

Q: Which one of the following points lies on the curver = sin 0 – 5. o (-5, 1) o (5, 0) (5, 2r) 2

A:

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A:

Q: ind all the tangents to the curve y cos (x %3D

A: Here we have to find the tangents on the curve y=cos(x+y)...........(1)     , -2π≤x≤2π parallel to…

Q: Find the length of the curve r = 4 – 4 sin 0

A:

Q: Find the length of the curve over the given interval. r = 2a cos θ, [−π /4, π/4]

A: Since, we have to find the length of the curve over the given intervalr=2a cosθ over the interval…

Q: Given, u=x3-y3. Which of the following is correct ? Harmonic Not analytic Not harmonic Analytic

A:

Q: This diagram shows a tangent TA with chord AB parallel to chord PQ.«

A: (a) To prove : ∆PAT is similar to ∆BAQWe can see that ABQP is a cyclic…

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: To use the geometry we will change the polar equation into the cartesian equation first.  For that,…

Q: Find the are of the sector on the specified interval  r= sqrt*tan theta  0 less than equal to theta…

A: Find the area

Q: Which one of the following points lies on the curver = sin 0 – 5. %3D TT o (-5, n) o (5, 0) (5, 2)

A: Put all points on curve, point which satisfy the equation , lie on curve.

Q: The equation of the tangent plane to the surfae ye+ = 0 at the point (0,-1, 1) is az+by+cz = Which…

A: Given yexy+z2 = 0    point (0 , -1 , 1)Let f = yexy+z2dfdx= yexy.y ⇒dfdy(0 , -1 , 1)=1dfdy= yexy.x…

Q: Given the following figure below. What can not be proven? 1. CX =DX root 3 2. CD is perpendicular…

A:

Q: Find the tangent of ZH. H. Write your answer as an integer or as a decimal rounded to the nearest…

A: We know that tangent of an angle is a ratio of opposite side to adjacent side.

Q: 1. Use Trigonometric substitution to evaluate f dx. Hint: Ju? – a² let u a sece.

A:

Q: (b) Using part (a), give one example of a harmonic function u(r, y) for points I, y E D = {(x, y) |…

A: For the solution of the problem follow the next step.

Q: (a) Suppose u(x, y) = 2x – x + 3xy? is harmonic, then find its conjugate harmonic v(x, y). -

A: The harmonic conjugate to a given function  is a function  such that is complex differentiable…

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: Recall:  L=∫abr(θ)2+r'(θ)2dθ We have, r=7sinθ+2cosθ, a=0, b=π

Q: Find the explicit solution of variables, Sinplify no loqarithms in y(x) by separation so that there…

A: A differential equation can be solved using the variable separation method. In this method, the…

Q: Find the tangent of LC. C 2/7 7/2 В Write your answer in simplified, rationalized form. Do not…

A: In a right angled traingle value of tan theta can be obtained by dividing the length of opposite…

Q: Consider the following. x = 3 cosh(t), y = 2 sinh(t) (a) Eliminate the parameter to find a Cartesian…

A:

Q: Find the points on the given curve where the tangent line is horizontal or vertical. (Assume 0sos…

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.