a) Given: y = (x² + e*)(x + 4) derive dx

Q: If f(z)=u(x,y)+iv(x,y), how do I determine dz? I have that the answer is dz=dx+idy, but I don't…

A: It's nothing to do with f(z)=u(x,y)+iv(x,y). Here z be complex independent variable. Hence , z could…

Q: Evaluate: a In(x + y) e-y. dy dx

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Q: dz/dy for z = e^xy

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Q: By algebraic substitution, the integral - dx dx is converted to: 4+x 2ydy (A y+4

A: Option a is the correction and other option does not satisfy the given conditions

Q: Find without using the Chain Rule and the ProductRule

A: We simplify the inner function using the properties of log.

Q: Q3\ using Euler method, find an approximate value of y corresponding to x€ [0 -0.7], Given = x(x +…

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Q: e*(1-cos(x)) Exercise: Evaluate S dx.

A: Now evaluate the integral, ∫0∞ex(1-cos(x))xdx Take the minus as outside and it is concluded as…

Q: (c) Show that (d/dz)z does not exist anywhere,

A: See the attachment

Q: 2) Obtain the DE with respect to x of (x - h)² = 4(y-k).

A: Sol

Q: af dy of f(x, y) = tan (x²y³ + 2xy)? What is the

A: Given:     To determine:

Q: Find the DE by eliminating the arbitrary constant  y = A+ bex

A: Given equation  y=A+be^x Where A & b are arbitrary constant.

Q: If z + In(e2x - e + e²) = 0 dz find at the point (0, 0) dx 2 0 -3 -2

A: see below the calculation and answer

Q: Q1-If x= cot- VE, y =, find d²y dx' dx2 at t = 2.

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Q: 1. Obtain the General Solution. Use reduction to exact. Simplify your fin y(y + 2x- 2) dx - 2(x +…

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Q: 6. General solution is y = x² In x + Ca² , EXERCISE 6. dy 2y = x? dx

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Q: Question The approximation of fxln (x + 5) dx using two points Gaussian quadrature formula is:

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Q: If y = In(2x+3) , then find dy at x = 0. dx

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Q: 7 xsiny dx + Cx²+1)cosy dy = 0, yC)=TT/2

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Q: Solve the Ro liowing B E 2 X + 2 -zey= zX

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Q: E valauate the JJ x +2xy +ydy dx when step size of x-0.2 and step size of use the Trapazaidal Rale…

A: given I=∫01∫02x2+2xy+y2dydx with  h=0.2 let x0=0.2 , y0=0.5 let fx,y=x2+2xy+y2 substituting the…

Q: b) Calculate dx for n = 6, using Trapezoidal rule. 1+x5

A: Trapezoidal rule:   where

Q: 1. a.) Use use the L’hospital rule lim(1+* dy b.) Use Devirative Rule to search dx from the equation…

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Q: 14) find the respect of y with respect to x Y=(6x+5)^x dy/dx=?

A: Given function: y=6x+5x Taking log to the both sides logy=log6x+5x We know that logxa=a log(x) So,…

Q: B. Use Greens Theorem to evalute é yx dx + x*dy as shown bele Left Half of (0.5)

A: Introduction: Let C denote the positively oriented, smooth, and simple closed curve in a plane and D…

Q: Given tanh(x)+ tanh ¯' (y) = 1, show that, 1- y? 1 – x² dy dx

A: Formula,ddxtanh-1x=11-x2Note- Since multiple questions are asked, I am answering the first question…

Q: f [Mesin(2x) dx = e$in(2x) + C, then the M is equal to- If

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Q: 2. If f(x,y)= te Vy of=D0 then show) that 49 c) of af =0 dxay

A: Consider the given function. fx,y=1yex-y24y (i) First, we have to show that ∂2f∂x2-∂f∂y=0. First,…

Q: If f(x) = – x Find: S",(f(x))² dx That is find S"(: ,(1 - x)?

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Q: Finf y' if x=Arccos(1-t), y=/2t-t2.

A: We can find the answer using chain rule as below.

Q: 6 If the substitution y = xº is made, the 64 3√√y 3 + √√y integral [ 1 dy will become

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Q: d cosh z =sinh x dz صواب ihi

A: Use the formula of coshz and sinhz in terms of exponents.

Q: Find the G.S.of the DE. (ytu dy=D0

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Q: 2. In each exercise, obtain the particular of solution. a. xy dx + 2(x² + 2y²) dy = 0; when x = 0, y…

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Q: 2- is the D.E:(3x² + y cosx )dx + ( sinx-4y )dy = 0 | a- - Exact b- linear D.E (show that)

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Q: 1. a- Find a result by using variable separation for dy dx b- y³y+x³=0

A: Note:- These are multiple questions and acording to our company guideline we can do maximum 1…

Q: The of the function y= e sin(3x)- In(5.x +2x+1) dx at (0,0) is: А. О В. -1 С. 1 D. 3

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: 4. Using homogenous D.E approach, solve (x³ – Зху?)dx %3D (у3 — 3x2у)dy. (v³ – 3x²y)dy. | 2 (ardai…

A: The given differential equation is; (x3-3xy2)dx=(y3-3x2y)dy.

Q: t seel dx

A:

Q: If a = 5+ti and y = 3t - t then dy at t = 1 dz is :

A: as per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1) dy…

A: Using differentiation

Q: Given tanh(x)+ tanh (y) = 1, show that, dy 1- y? dx 1- x2

A: We can find the required answer as below

Q: 1. Use residues to evaluate 1 : xe dx , (a>0).

A: Let fz=ze-zz2+a2 The poles of the function fz are ±ai Choose the contour C consisting of the real…

Q: (b)/ Use the Trapezoidal Rule with n = 4 to estimate ſ,(x3 + 1)dx.

A: To find: ∫-11x3 + 1dx using trapezoidal rule with n=4

Q: 3. For x= In /t y=t2, find y'-y"when x=0.

A: To find: The value of y'-y" when x=0 . Given: The value of function are x=ln(t) and y=t2. Formula…

Q: In x Find y' if y = e3 1 – 4 In x Based on your work from (a), evaluate - dx. -5

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Q: B4. Evaluate e* sin x dx by using integration by parts method.

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Q: Find the antiderivatives |x In(x²) dx + sec? x dx CO X dx sin5

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Q: Q4/ Evaluate (xy + e") dy dx using Three point formula in x,y-axis and two point formula in z axis

A: You must have an basic idea of double integral to solve this.