Q4\ If A(x,y, z) = 3x²i + 3zj – 3xk find the Div (Grad A). %3D |

Q: 6x2+7y2=C satisfies 6x+7yy' given the inital condition y=4 when x=6 what is C.

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Q: If Z=x+iy and 12/=/2-81 of *= Hhe Value %3D

A: Given that       z = x+iy  and |z| = |z-8| Here we have to find the value of x .

Q: Find high order DE 6. (D4-5D² - 36)y = 0

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Q: To the reci max z Ax1 +B x2 A=6 s.t. 2x +4x 2 12, B=1 -X1 + 2x2 S 2, X1 20, x2 Free.

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Q: compute ∫_D 2ydx+3xdy, where D is described by 0≤x≤1, 0≤y≤1

A: Green's Theorem: Let C be a positive oriented, smooth, simple closed curve. Let D be the region…

Q: d (7) Vtan²s+ 21 dt = dx

A: Explanation of the answer is as follows

Q: 3x* – 4y* = C

A: The given equation is: 3x4-4y4=c

Q: Find the general cowtion of the die. y9) + ya) - 24 =-e (9+67x+17 x²) + (861nax - o cosex) „(2).…

A: The given differential equation is , y(3)+y(2)-2y = -e3x(9+67x+17x2) +…

Q: 10) W 3x -4 M x+3 • 2021 Kuta soft ware LLc. AIl righis reservet Made with Inf inite Geomery. 11)…

A: In a parallelogram, opposite sides are equal to each other.

Q: Q. / Standx dx 3 None 2log|sec4x| + c 3 8log|sec4x| .+ c 3 2log|sec4x| + c 4

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Q: 4. f(x, y) = 10x²y* – 6xy2 + 10x2; fx(x, y), fy(x, y) %3D -

A: Consider the given function as fx,y=10x2y4-6xy2+10x2

Q: dz Find - if z = (9x + 5y)°. dy

A: we can find the derivative as below

Q: - r)rdrde 32(V2-1) 16(VZ-1) c. VZ-1) 4(VE-1), S(V2-1) a. d. 3. 3 3 e. 3.

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Q: Find an antiderivative of ƒ(x) = 5x4 .

A: fx=5x4

Q: Z. WY = %3D

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Q: f(x, y) = In(4x + 3y) Calcule

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Q: Integraate :S, 22+x+! d>x 2.

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Q: 22) Find 2 positive numbers xby WHh xY=50 SUch h that 2x+Y is minimized. Round to neakest tenth.

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Q: 4y² – 25 -dy

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Q: Find the antiderivative

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Q: dz Find if z = (4x+ 9y). ду dz ду

A: Topic- partial differentiation

Q: 3- Suppose that s(x)dx 5. Find A- B- S V3 f(2)dz D-

A: Definite Integral of function f(x) in the interval of [1, 2] is 5. The function remains the same for…

Q: ral soluion of qineral xy" + 2y'=6x Find the

A: We will first reduce the order of given differential equation

Q: S (x+Sy+wz ) dzoly dz 2 3x X-つ

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Q: (b) Differentiate (Vx+ 1) with respect to x. 2/3

A: as per our guideline we can solve maximum one question you can repost other questions

Q: (4) (b) 10tsin(5t²- n/4)dt (4) (c) S 12(x³ + 2)ex¹+8x dx

A: We have to evaluate the integrals.

Q: .3 S(3 – e3*)²dx

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Q: . Use the method of Lagrange multipliers to show that for x, y > 0, we have a" +y" > (팔1)" 2

A: We will first try to minimise (xn + yn)/2 using Lagrange multipliers then show that its minimum…

Q: :Q3 Classify PDEs below и ди y2 и + и = ue 5x — - ду

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Q: S sec 2ydy

A: Topic:- integration

Q: 3(1 + P) = 2ty(y³ – 1) dt %3D

A: Let us consider the differential equation dydt+P(x)y=Q(x)yn It is known as Bernoulli's equation…

Q: 3. Obt nin the parh cular folu tion 9. xdx - ydx + 3x dy +ydy = 0 ; wun x - 5,4= -:

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find dw. If w=2x3 +3x2 y-6y² 3 dw=(x2+6xy) dx+(3x2 -y) dy Ob dw= (6x2 +6xy) dx+ (3x2 – 12y) dy

A: This question is taken from the partial differentiation in which we have to total derivative of the…

Q: 4- Evaluate the variation of : tf (2x2 + 3x(t) + 4)dt J(x(t)) : to

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Q: yz 4. II »z dr dy dz Jo

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Q: f Lan 2X e *3 of +sec2X Pinel dy o

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Q: What is the discriminant of the PDE?    4d2/dy2=-3du/dx-4u

A: the discriminant of the PDE is :

Q: 6. Differentiate y with respect to x using A-method. x-3 a. y = X b. у %3D V4x + 3

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Q: ationalize the d V49

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Q: Let X = n(µ,4) and Var(2x) = E(4–7x) find %3D H.

A: Given: a random variable X follows normal distribution. Mathematically, X~N(μ,4) The expected value…

Q: integrate C.

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Q: 4. V21+4:-z dz

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Q: Minimize c=s+ 2t subject to 4s +t2 270 2s +t2 190 s+ 3t 2 330 s20, t2 0. C = (s, t) =

A: The given minimize problem is C=s+2t subject to constraints, 4s+t≥2702s+t≥190s+3t≥330s≥0, t≥0   Then…

Q: (zin z + 5)dz

A: The given integral is [xlnx+5] limit from 1 to 3.

Q: у" — 4y' + у %3D ex + 15

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Q: Evaluate S. (x – y)dx + xydx where C is the y = 2x2 – 1 from the point (-1,1) to the point (2,7).

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Q: What is L[y] if y = u3(t) (t- 3)2? %3D L[y] = e3s . - 3 O Lly) = e3s. 2 L[y] = e-3s. 2 O Lly] = e-3s…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.