3 9-r22 1 dy dz dr 9-r2 0_æ²_22 (x² + y² + z²)1/2

Q: dz f1-42-223)2 3 4[3-2(2+パ) a. In 3+ JE (z+1)/ J3-2(241=+C 3-4,(2+)? 3 b. 4[3-2(2+1=)] C-A(24)?…

A: Given ∫3z(1-4z-2z2)2dz ∫f'xfxdx=lnfx+c

Q: 1.0 1,0 -1 =) 5f(x) dr = %3D =) L 5f(x) dr =| =) S* 5f(x) dr =| ) | 5f(x)| dx =|

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Q: 3. Find the solution of the initial boundary value problem (IBVP) Un = Uxx for -0 0 u(x,0) =…

A: Given a hyperbolic equation, utt=uxx, -∞<x<∞, t>0 with initial and boundary conditions as…

Q: 3. (3y² + xcos xy) + (3x² + ycos xy) = 0 dx a) y + sen xy + x³ = 0 y² + sen xy + x³ = 0 y² + sen y +…

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Q: 4. Find the solution of the differentia (10 Points) dy ! = 2x2 dx %3D O y = x³ + O y = x³ + c O y =…

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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: ne particular solution is/are ocated at x = . Choose only one of them if here are 2 or more…

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Q: 0 0 0 2 1 0 0 0 2 0 0 2 2 1 Find the general solution to x' = Ax if A %3D

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Q: 4. y= 5e, y-s+ax-3x between x-0 and x=1 about y= -3

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Q: X(z) = z(z+2) (z-1)(z-3) x(n) = u(n) — 223¹u(- -n-1) x(n) == Option 3 3 5 )=-u(n) + 3"u(n) Option 4…

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Q: Find L(x). 2y -a = 3t y+z' = 3e z (0) = y (0) = 0 = (x) T0 (s+1)(s–2)(s²+1) OL(z) = 3s2 3(s-1) %3D…

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Q: Using Cramer's rule to solve [x + y = 8 lr - y = -2, we obtain and y = 3 2 4 5 1 1. 3 1 1 ||

A: To solve x+y=    8x-y=-2

Q: 6) calculate In (2e°)= 11 2= 0.7n 3= 1. || ln5=1.6n7=20 %3D n(2e°)=X L ex =In 2

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Q: 3 (D2 + 4)y =- Ost<3 3t +2 t23 y(0)=0, y'(0)=1 Find L{y} °L{y} = 1 3. 3e 3s Se-3s 82+4 s(s2+4) s (s²…

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Q: 6 Maximize Fenoi Z = 2x1 – 6x2 subject to anole 3i X1 – x2 < 4 - -X1 + x2 < 4 X1 +x2 < 6 X1, X2 2 0

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Q: 9. between z = -2.09 and z = 1.72 Area: 10. to the left of z = -1.27 and to the right of z = 2.86

A: To find the required areas we use Standard Normal table.

Q: 1. Verify that y = e²x + 3xe²x is a solution of the ODE y" - 4y + 4y = 0. (Show all work when…

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Q: kx 4+x² If k > 1, evaluate O ka -In|x² + 4 +C 2 Okx -arctan (2x) + C 2 Ok In(x² + 4) + C O arctan…

A: Given: I=∫kx4+x2dx   ...1   As we know the common integral. ∫1ax+bdx=1alnax+b+C

Q: 5s +3 3) Find L'{Y(s)} where Y(s) = (s+1)(s+2)(s+3)

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Q: Find Pr (|w| < 0.2)  where W ~ N (-1,4)

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Q: 4) Solve via separation of variables: u(0, y) =0 ди -(2, y) = 3sin a'u a'u +5 sin =0 ; 6. S0<x<2…

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Q: əz ax+by+sin(ax +by) show that b əx Q5-A) If z = (ax +by)² +e+by+sin( ax a Əz dy

A: The given problem is to show the following condition for the given multivariate function of z.

Q: 1 Let y = x2 g(x) + 6x -1 Find at x = 2 given that g(2) = - 3 and g '(2) = - 2. dy dx Enter an…

A: Given

Q: 5 By separation of variables, Solve the followin PDES :- du dt d2u dx2 @ o U (0₂t) =(4,t) = G u(x,0)…

A: Given is the Partial Differential equation ∂u∂t=2∂2u∂x2…

Q: 2 2х-4 2у — 1 dydx x + 1 ) Q2. Evaluate the double integral

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Q: Show that r n2n-1 r=0

A: Want to  prove:    ∑r=0n rnr=n2n-1

Q: /16–y² /32–2²-y² n[L 2² + y* + z®)dzdzdy in nvert 1²+y² •1/2 4/2 -/2 Jo п/2 " T p* sin ódpdődý •4/2…

A: from the integral limits are as  follows 0 ≤ x ≤ 16-y2 0 ≤ y ≤ 4  x2+y2 ≤ z ≤ 32-x2-y2

Q: 3- Let µr1 = 2 in region 1, defined by 2x+3y-4z > 1, while µ2 = 5 in region 2 where %3D 2x+3y-4z <…

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Q: 1. The loop of y² = x * (4 - x) 2. у %3D 6х — х?, y = x² – 2x - 3. у %3D 2х y2 + 4x – 8 = 0 - 4. An…

A: Question 4 : Arch of y = (1/3)sin(x/3) First find out intersection points :  y = 0 (1/3)sin(x/3) = 0…

Q: 10. Integral 2-t dt

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Q: a2u a2u =4 at2 au(x,0) où 0 sxs2 with (0,t) = u(2,t) = 0, = 0, %3D %3D %3D at x if 0<x <1 2-х т u(x,…

A: utt =4 uxx               :  0≤x≤2 u0,t = u2,t =0utx,0 =0   ux,0 =x      : 0≤x≤12-x : 1≤x≤2

Q: 23. x*y" + xy' - y = In x

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Q: (x+1)(x-2) 28. f(x) = %3D o(x-2)(x+2)2 ald worl m1 30. f(x) = O 2+3x %3D %3D 4* - 6(2*) +5 32. f(x)…

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Q: 5. (a) Solve the cauchy problem given by x²ux + xyuy + xu = Xx-y where (x, y) + (0,0) if u(x, xln x)…

A: Given x2ux+xyuy+xu=x-y where x,y≠0,0 if ux,xlnx=-lnx, x&gt;0

Q: 7) -U(X-2)(x+3)" (5x-1)(7x+ 2) 3х+13 6) 57 In7x+2+c) (ans.: In 5x 2х -3 7)Sー (ans.: -Im,x-1+ Im,x-2-…

A: ∫1ax+b dx =1alnax+b+C Note :As per our guidelines , we can solve first question .Please repost…

Q: 10:29 ll LTE O True or False 11. If two figures are congruent there is always just one way to…

A: Statement is given  We have to define it is true or not

Q: 21. The equation x - 2·* - 0 has a root in the interval A OS x s1 B ISXS 2 € -1s x < 0 D -2 < x s-1

A: Exponential equation

Q: x²y' + 2xy = In(x), y(1) = 2 y = In(x) 1 2 + 1. 3 + - y = -In(x) O Option 1 Option 2 1 1 1 1 1 2 y =…

A: We are given first order non homogeneous linear differential equation which we will solve by first…

Q: 6. Find the general solution of (x + 2y - 1) dx + (x +2y +5) dy = 0 х +у - 6 In(7 -х - 2у) 3 x - y +…

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Q: 2 - = 3t y+ x' = 3et * (0) = y (0) = 0 OL (x) = 3s2 (s+1)(s–2)(s²+1) 3(s-1) OL (z) = 76+1) (28²+1)…

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Q: Solve the DEQ given the initial condition (4,-2). Graph it on the slope field. 10 9 1 8- Let…

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Q: c) Solve the boundary value problem given as y" + = 1, with boundary conditions y'(0.5) = -0.0283,…

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Q: a²u ax² a²u =1- x for 0 0, - u(x, 0) = x²(1 – x) for 0s x s 1, du (x, 0) = 0 for 0 s xs 1, at d" (0,…

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Q: 1.1. Show that Y(n) max(Y1, Y2, ..., Yn) is sufficient for 0.

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Q: finde general Sonotion 1- y' = See'y 2X-1 %3D 2- 3-Xy=Y+2x $ in?

A: This question can be solved by applying the concept of differential equation.

Q: f(X1,X2) = f(X1).f(X2) X1~N(H1,0),X2~N(H2,0 are not indepen If dent then ylgn

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: x² In y + y In x = In xy

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Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.