2. 1. f (x) = x° – 4x – 5 g(x)3Dx5 a) Find(-)æ x + 5

Q: Find impicitly, tf e*(eУ — 1) + sin(2x + 5у) %D In(V7) - - сot(2x) y+2

A: Given function is Differentiating with respect to x by using product rule ,we get

Q: 4 b. [√x ln xdx, 1 4 ㅠ C. fx√4-xdx, d. fx sin (2x) dx. 0

A: Solve the following

Q: 1) f(t) = e3t+ sin²t +6 cosh /7t -3t²

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

Q: f os 7x cos 2x dx

A:

Q: 4. Show that y=e²* sin 3x satisfies the equation: y" – 4y' + 13y = 0 %3D

A: Topic = Differential equation

Q: Q1: If Z= x^3+y^4+(x sin y)+ (y cos x), Find Zxx? Zyy? *

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Q: 3. If G = (2x²y – x*)î + (e*y + y sin x)j+ (x² cos y)k, find: %3D дхду

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Q: e" sin°(2x) (d) y = In 2x2 + 1

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Q: dz dz and ду Suppose z is a function of a and y, and tan Vy² + x² = 2e6y. Solve for

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Q: b) Z = Arctan ( x² /y³)

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Q: IV. Suppose z is a function of x and y, and tan yy² + x² = z*e6y. Solve for dz dz and

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Q: Solve the particular solution of (D2 + 1) y = sec (x) tan (x) using variation of parameters

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Q: 3.4.4 Evaluate ff sin(x + y) dx dy over the triangle whose vertices are (0, 0), (2, 1), (1, 2).

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Q: 2.2 Use the definitions of hyperbolic functions to solve for A and B if: 5e* – 4e* = Asinhx+B coshx

A: Definition used: sinhx=ex-e-x2coshx=ex+e-x2 Consider the given equation as 5ex-4e-x=Asinhx+Bcoshx…

Q: d²y dy and dx Find if x = sin 3z and y = tan23z dx2

A: It can be observed that both the variables x and y are the functions of  z, therefore to find the…

Q: c fx) = at (4, 2) 3x – 4 d y=x In x at (0, 1) sin3x at y =- x? 4 e T 2

A: Part(c): Given function is, fx=x33x-4 at 4,2 To find the gradient of a function (which is a vector),…

Q: 7. Solve the following Cauchy-Euler equation d'y - 4y = 0. dx - %3D dx

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Q: B) If f (x, y) = tan (2x – 3y) find дх ду?

A: Given function is fx,y=tan2x-3y

Q: 1. f(t) = -2e-14t + 5 Cosh(4t) 2. f(x) = 4 Sin(7x) + 480

A: We will use Laplace transform of some standard function to solve this.

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); u =

A:

Q: IV. Suppose z is a function of r and y, and tan Vy² + x² 2e&y¸ Solve for az az and dy

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find a positive value of k for which y=cos(kt) satisfies y''+25y=0.

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Q: t Cos(4t – 2019) 4.) f( 1)=

A: Given that: f(t)=tcos(4t-2019)

Q: SV1- x2 sin-1x dx

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Q: •2/3 Find dx. Hint: try either x = 4 sin 0 or u = 16 – x² as a substitution. 16–x²

A: Topic = Integration

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); U =

A:

Q: Find the solution of the equation a²z a²z + cos y V ax² dy² which tends to zero as x→∞ and has the…

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Q: Q2 Q2/If y = (x³ + 5x² + 1)3 + Jsin+/cos³Vtan3x2 find y'

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = i

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Q: Q6A)If y = sin-¹ prove Zyy + 2 = 0

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Q: Q.2 Find [(x' +5x² – 2) sin 2.xdx . c Inx

A: According to Bartleby Q&A answering guidelines I can answer only one question

Q: Solve by finding an I.F 1. xdy – ydx = (x² + y² }£x y - sin x 2. dy + -dx = 0 ......

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

Q: Obtain the general solution of 4dx = xVx² – 4dy. Express your answer in terms of cos function

A: The general solution of an ordinary differential equation is the an expression for the dependent…

Q: (4D3 + D)y = e2* A. y = c1 + c2 cos 0.5x + c3 sin 0.5x +e2x 33 B. y = c1 + c2 cos 2x + c3 sin 2x…

A: From the given problem: 4D3+Dy=e2x The auxiliary equation is: 4m3+m=0m4m2+1=0m=0  or…

Q: Solve for the particular solution of the ODE y" + 4y' + 3y = sin(e^x).

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Q: 5. (a) Find all functions y = f(x) satisfying dy/dx = sin(2x) + x. (b) Find the one function from…

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Q: b) dr cos² #√5 + tanz c) ₁ dt (3-5t)²

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Q: a²f Compute , and Je Te дхду f(x, y)= x'y² – sin 2+ xe" əx' əy

A: Explanation and solution is given below....

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); i 5 .5 и 3

A: The function is given by  fx, y = sin8x-5y The point is x, y = 5, 8 The unit vector is  u = 35i-45j…

Q: If y = (x – a)/2ax – x² + a² sin¬'(÷ prove that y' = 2/2ax – x² a is constant.

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Q: IV. Suppose z is a function of r and y, and tan y2 + x² = 2*e. Solve for az dz and %3D dy

A: To solve for dz/dy and dz/dx.

Q: 8. (e sin y + 3y) (3x - e" sin y)y' = 0

A:

Q: 2.2 Use the definitions of hyperbolic functions to solve for A and B if: 5e* - 4e* Asinh x+B coshx…

A: Consider the following equation:…

Q: 4) B: Solve for x: az + vx-4 + y sin2x) < 4cos2a laxdy

A: Given - ∂2∂x∂y y3+x-4 + y sin2x &lt;4cos2π To find - the value of 'x'

Q: Express = In(4t), y = 7 – t in the form y = f(x) by eliminating the parameter. y =

A: Given equation is as below: x=ln(4t)y=7-t

Q: Q3.If f(x,y)=sin(x-3y) + sin(x1 find: af 2x and af dy

A: We can find partial derivative with respect to 'x' and 'y' .

Q: Then we have from equation (1), -k-1 II Pi=1 k-1 nk-1 i=1 i=1 Pr (-1)*-(1) (-1)–1 (-1)k Yk=A - Where…

A: Answer

Q: 1. f(t) = cos(6t) 2. f(t) = (e^(8t)) cosh(3t) 3. f(t) = (t^2) e^(-4t)

A: Lcos(at)=ss2+a2 Leatcosh (bt) = s-a(s-a)2-b2 Ltneat = n!s-an+1