dy - = 2/y- 5in|Vy+ 5| + c Vỹ+5 A) True B) False

Q: Show the only soution to ax = 1, a + 0, is x = a^-1|

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Q: 5. If u = e1#1+az#2++anIn, where a² + a³ + · ·..+ a = 1, show %3D + = U dx?

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Q: Suppose that f(æ, y) = e" = e-3z? - 4y? +y

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Q: 2. Cuven that 7, = -2 +ui, Z= -2i + 3 and E, - |-i. Gvaluate the followshng %3D 2 | 국 2

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Q: S = In sec 3x| + C 13. z sec² 3x dz %3D 3 - tag 3z,- å

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Q: if y = secx prove that y^2+y=2y^3

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: 8z Find at (2, -2, 1) if By z' +y +z2 = 6xz +6yz +21 eej49 1.

A: Given x2+y2+z2=6xz+6yz+21

Q: The line that passes through the points (2,0), (0,1) is x+2y = c, where c = 1. O True False

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Q: 15. In AXYZ, XY YZ and m/XYZ = 46*. %3D 46

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Q: for w = ze(zy²+2:). Do not include =" in your answer.

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Q: - If y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

Q: Solve min udr, subject to u(0) = 0, u(1) = 1, ur'dr = c %3D =C.

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Q: af Given f(x, y) = In(7x² + 9y²) then

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Q: If (x, y) = (-V3, 1) , then find r and 0.

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Q: Ql if (x,y,z) =o and Z"=x+Y find d2 (using di f Beren tials concept)

A: Given  If f(x,y,z) = 0 and z2 = x + y

Q: If b is dviisible by a (a|b) and b in different than 0 then |a| is less or equal than |b|

A: The given statement means the following.

Q: In Trapezoidal rule method Error Bound: kf"(a) <ES kf"(b), where k (b-a)3 True False О

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Q: Show that d(y,u)/dv = (1– v²/c)3? for y, = 1//1- v²/c?. %3D

A: Given: γv = 1/1 - v2/c2

Q: Use Cramer's ru;e to fins a solution: 5x+4y=12 3x-6y=24

A: System of equations are 5x+4y=123x-6y=24

Q: Using the substitution u = 2x – 1, prove that - -3 8 dx 1 (2x-1)3 25

A: The given integral is ∫13x(2x-1)3dx Put 2x-1=t⇒2dx=dt when x=1 then t=1 and when x=3 then t=5 So,…

Q: af (2,0) ay f(x, y) 3D хетУ + 5у%; af (2, 0) = Əy

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Q: Solve Ut = Urx, x > 0, t> 0, u (x, 0) = f (x), u (0, t) = 0.

A: Given partial differential equation isut=uxx,     x&gt;0,     t&gt;0ux, 0=fxu0, t=0

Q: et A be 4X4r nas non-brivial . -son-

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Q: s) Given u(r, s) =r2 - 2s2, wheter= and s = y? - r, compute for du

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Q: ) s how that the line af intersection f the Planes X+2y-22%= 5 and 5x-2y-Z=0 is Paraliel to theline…

A: Solution is written in below steps.

Q: If x + y + z = 12 & x² + y² + z² = 96 & !.!,!= 36 then value -+-+ -%3D X y of x³ + y3 + z³ is

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Q: 3. (z, y)(1.5x, 1.5y) A' will be located at ( B' will be located at ( C' will be located at (

A: We have given the scalar factor i.e . (x,y)=(1.5x,1.5y)

Q: 27 - Dans une étude, l'équation de régression linéaire simple a été trouvée comme y = 3,02 - 10,30 *…

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Q: Q3: A. Find Wer if W = f(x, y) {x = reost, y = rsint W₁,

A: From chain rule we know if w=f(x,y) and x=g(r,t) and y=h(r,t) then, ∂w∂r=∂w∂x∂x∂r+∂w∂y∂y∂r

Q: af(x, y) If f(x, y, z) = , then is equal to dz (y – 2)² (y – 2)? O 1 2z – x – y (y – z)?

A: Given problem:-

Q: If i = xi+yi+zk then grad (r") is equal to

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Q: Find the indico 6. 2. 3+ 2 1..2+4+8+ 27 t. 4. 3. 12, (4)"- n= %3D1 2.

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Q: (i) Evaluate S(z + 5i) dz where the path is the line From z = 1 to z = 2 +i

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Q: In Exercises 53-58, compute the derivatives indicated.

A: Here given as fx, y=3x2y-6xy4 Now ∂f∂x=∂∂x3x2y-6xy4=6xy-6y4∂2f∂x2=∂∂x6xy-6y4⇒∂2f∂x2=6y

Q: 3. Assume that z= 2(r.y) and ee = ryz Find and

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Q: if y=Asinx+Bcosx then prove d2y/dx2+y=0

A: Given,

Q: In AXYZ, PQ I| XY.If XZ= 15, YZ= 12, and ZQ = 8, what is ZP?

A: given XZ=15, YZ=12, and ZQ=8What is ZP?

Q: O The madices of cervadere af r= éat any poind Y, is (@) r?VTt (b) rvite? (C) Vitaž (d)

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Q: {(x, y), 4.x2 + 9y² < 36} C R2 ected? pathwise connected? Justif

A: Connected and path connectedness

Q: Solve Utt currrx = 0, -0 0, %3D u (x,0) = f (x), Ut (x,0) = 0, -0 < x < ∞ ||

A: Given that,utt+c2uxxxx=0-∞&lt;x&lt;∞t&gt;0ux, 0=fxutx, 0=0The pde is solved as shown below

Q: If ø(x, y, z) = ry²z find grad ø at (2, – 1, 3).

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Q: Q- show that yo+(?) sy + (2) B²y_₁ = y + (1) DY...+ (1²¹) Ay -

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Q: %3D 23. f(x, y, z) = 2x + z? subject to x² + y? + 2z? = 25

A: Lagrange's Multipliers: The Lagrange method is used to maximize or minimize a general function…

Q: T= tanh (x+ 2y+ 3Z) %3D finds O Tyy @ Tyx 3 Txy Tz Tzz Tzx @ Tzy

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Q: 9. Find y if (a) y = 2" In (cot² (v7))

A: We are authorized to solve only one independent question, please repost remaining questions…

Q: vsin ax (02+4)4= sin x is the fun ction with y %3D

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Q: me succe LO SUIVE uie folnoWing 2 и (х)— | (x -t )u (t )dt 2 --

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Q: 4 - If w = x+ 2y + z? , x= , y =r2 + In(s) , and y = r2 + In(s) , and z = 2r aw find at the point…

A: Using chain rule the given question has been solved in step 2.

Q: 4. Show that 4= 3y'z' i+4x²:* j+6x°y°k is solenoidal.

A: