4. (4 – e 3*)³dx

Q: 21. Кх, у) 2х -у ys 4x + 6 5 * 4y s 7 2r + ys7 бу X-6y z 10

A: Step-1 f(x,y) = 2x-y            y ≤ 4x+6 ⇒ 4x-y ≥-6            x+4y ≤ 7           2x+y ≤ 7…

Q: .3 2- S(y² – 4y + 2 ) dy

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Q: 3. 2t t dt ST-t

A: To integrate the given vector function. ∫te2t, t1-t,11-t2dt...(1)

Q: a=t). CTaylon Serie) 2-X Ln +x) (MacLurinSeries

A: We need to find the Taylor series of f(x)=12-x at a=1. Taylor series of function fx at a is defined…

Q: 4. 5 Show that if y%= x+4 then dx (x+4)** %3D %3D 16. dx. 2 (x+4)² **n Hence, find the value of|

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Q: et dt 3/2 +8 e' +

A: Given integral is, ∫ete2t+8et+732dt. It is integrated by applying u-substitution method, Substitute…

Q: a+, 3. f(1)=1** +a cosh /21 +bsinh /21 f(1) =2cos" (21) +e² 4.

A: The Laplace transform of the function f(t) is defined as Lf(t)=∫0∞e-stf(t)dt, since the dimension of…

Q: Show that x +2 and oe) = *+6

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Q: 1.) Evaluate: S(2 + y²)²dy

A: We have to find integral

Q: 2. 17ァーーレス+ら)dx Sim pricy the anw ser =

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Q: y If z = show that = 0. x + y?*

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Q: 2 If In(ax)dx = 3, then a = %3D %3D 1 4 4 e4 4 ез 4 O None

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Q: 26. у" + 4y' %3D sec 2x

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Q: 5. (5 – x)² * 6 Show that if y=3-x then %3D 6. . (x-s) _ xp 1. dx. 3 Hence, find the value of , 2(5…

A: In differentiation use quotient rule In integration use substitution

Q: 13. Find ML. J 3x + 11 K N 45 7, 10x - 12

A: According to guide and we should have been able to do only one question at a time #13

Q: 2x2+3x−20 has root(s) at x=

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Q: 4x obtain the section of the equation Ex xl with the condition u oon X4

A: Let us consider the given PDE is P(x,y,u)ux+Q(x,y,u)uy=R(x,y,u) The equation is solved as Determine…

Q: -5-S"S, ((m-3)x²+m(m -! x- Yy)-4myx] dydx 2,3m

A:

Q: 2) Show that (1 – x²)P",(x)P'm(x) dx: 21(l + 1) Sim• 21 + 1

A: Given:-  ∫-11(1-x2) p'l(x)p'm(x)dx=2l(l+1)2l+1δlm

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

A:

Q: Find the length of the curve y = In(e - 1) – In(e + 1), In 2 sxsIn 3.

A:

Q: (e) Yk+1 +Yk = 1/k(k+1),

A: Given, yk+1+yk=1kk+1Substitute:yk+1=y'yk=yEquation formed is:y'+y=1kk+1A first order separable ODE…

Q: 9. If x2-xy + y2 = 3, find y' and y", %3D

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Q: s at x =-1 and x = 2

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Q: 3. If 4=(x+2y+az,bx– 3y-z,4x+cy +2=) is irrotational. Find constant a,b,c.

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Q: 1 B (m,n) = m-1 (1-x)"-ldx %3D

A: Concept: By definition of Beta function

Q: If 8(x) = [e²-m (21+ - dx S[e²-In (21+1) ]dt, find g(x). -2 A e-In(2x+1) 4 B (2x + 1)² 2 Ⓒ (2x + 1)²…

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Q: 4. y=6-ax-x", y = x+l6, about the a %3D | yaxis

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Q: S F(s) %3D (s+5)6

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Q: 2): Consider the DE y" – y" – 6y = 0 -

A: Follow the procedure given below.

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

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Q: S(2 + e2*)³dx

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Q: 23. If exy = 3, then what is Y at the point (1, In3)? dx -In3 3ln3 In3 -4In3

A: Given:- exy = 3 To find:- dy/dx at point (1,ln3)

Q: find The Six Solutious of The eq- 6 Z+27+2

A:

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: B/let Flx)=[X]-X,x E(-2,2).which valuesof x o E(X) continuaus?

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Q: x2 1 dr dy = a° In(1+ x² + y? 3

A:

Q: a. 2,526sinx + 2,526cosx Yp 29 b. yp 89 3 M 7,930sinx + 7,753cosx 91 3 = c. Yp 3,290sinx +7,753 cosx…

A: We will find the particular integral.

Q: لله √ √³ √ √² zysin(2² + y²) dz dy −

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Q: 2 2 2 1+ 2 t3十 Cn)和 9 Prove that

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Q: 4 In GL(2,Z13), det 1 4

A: We have to find the determinant using GL(2,Z13) That is, instead of usual addition and…

Q: 4. So -dy Vy+1

A: To evaluate: ∫01yy3+1dy Substitute y3=u2⇒13y-23dy=2u du⇒13u4dy=2udu⇒dy=6u5du. As y→0⇒u→0, y→1⇒u→1…

Q: dt | sec? 3 3.

A: Given: An integral ∫sec2t3dt Integral of sec2x is given by∫sec2x=tan x+C. Using the formula…

Q: + 4 (A In(x² + 4) + C B arctan() + C (C) jarctan(;) + C -arctan() D arctan () + C

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Q: 4 In(t) dt

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Q: 2/3 If y = xl/3 + 2 dy then |z */0 =-8 dr

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Q: (1,1) Evaluate [ (3x²+4xy+ix)´dz along y=x² (0,0)

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Q: 2 4 Mx(t) = -e+ 3t e' + e" + %3D 3 15

A: Given: Mxt=13et+415e3t+215e4t+415e5t

Q: , у"+ бу'+ 9у 3D 0; x = 0, y = 0 and x = 0, y' = 3 = Ans. y=3 x e-3*

A: