.2 ax + sin b + sin cx + sin dx = 4. Find Q 9) a, b, c, d are constants such that lim0 %3D 3x2 + 5x1+ 7x6 the value of the sum a +b+c+d. (Hint: think what happens to (xtx?) when 0.)

Q: Given that cos(x) = (-1x2 for e<xc than a powr saries of cas(x) %3D ie e (2n)!

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Q: (b) D₂f = 2 cos(xy + 2z) Dzzf = -4 sin(xy + 2z) Dzzyf = -4x cos(xy + 2z)

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Q: Show that 0, if m if m + n sin(nx) sin(mx) dx T, = n IT

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Q: 2.) If H (y) = cos y – sin y, find H (0), H (n),H (T), and also show that H. n+ x) = H (n - x) = -H…

A: The solution is given as

Q: 7 y=tanx show thats y" = -2Siny cosy 1f y=e Snbx show that:

A: Dear Student, according to the Bartleby guidelines, we can answer only first question if multiple…

Q: Use Picard's theorem, find the largest interval for which the IVP (x2+3x-4)y"-tan(r)y'+e*y=7,…

A: Given: (x2+3x-4)y'''-tan(x)y'+exy=7, y(-1)=1

Q: The integral / 2/ (*) cos(2*) dx takes the form k cosu du when u=2* and f (x) =x – 5. what is the…

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Q: x’y? If z , show that x=+ y- 3z x+ y ôx ây a²z ô²z = 0 if z= Tan 2.xy x² – y? Show that âx² ' ây²

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Q: Find Duf at P. 3 4 f (x, y) = sin(3x – 4y); P(4,3); u = i j %3D - - NOTE: Enter the exact answer.…

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Q: If z = x2 + y² and x t cos 2r and y = r sint, then %3D a2z is at2 (A) 2 cos²(2r) + 2r? cos?(t) – 2ry…

A: Given  z=x2+y2      and x= t cos 2r ,y= r sin t First substitute x,y values in z  Then derivative…

Q: 8- Evaluate a) Sz? + 4 sin(8z) dz 1+9cos(8z) бх- х2 b) S 3x. csc² dx x3-9x2+8

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Q: 2. Find the area outside the inner and inside outer loop of the limacon r = 4 sin 0 - 2 101

A: The equation for the Limacon is r=4sin θ -2 The graph given is

Q: If y=C,cos2x + C,sin2x+2sinx is the general solution of a certain nonhomogegeous LDE, which of the…

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Q: 2a + acoth 2z ) dz \sin 3z a/2

A: We are given the integral: ∫a22a1sin 3z+a coth 2zdz Let I=∫a22a1sin 3z+a coth 2zdz I =∫a22a1sin 3z+a…

Q: 2/3 Determine the length of x=| for 0<ys2. Assume that y is positive.

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Q: d) solve to 1l o wing equan on. the differenti al 2 dy 3y = 3 n2 + 5 %3D

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Q: If ſ cos* xdx = Ax+B sin 2x+C sin 4x +D, then {4,B,C} equals S3 1 1] 18 32 4 [3 1 1 (b) 8 4 32 ƒ1 1…

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Q: 3. Show that the equation for G(r,ø) can be separated by choosing G(r,ø) = R(r)P(ø) into OR Rar ar 1…

A: Introduction: The Laplace equation is one of the most important partial differential equations. It…

Q: O Consider d = - CoSk; yeo) =0,iylo) Reduce he abore initial vaeue problem To be roltera entegral…

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

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

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Q: (a) Suppose x E Q with x # 0 and y E R – Q. Show that their product ry is irrational.

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

Q: For z + y, lim ()(1,1) Va - A. 0 В. 2 C.1 D. Does not exist.

A: This is simple question can be solve by rationalising the given function Solution is given below

Q: 7 Use the Intermediate Value Theorem and Rolle's Theorem to show that the equation 2 = sin z+1 has a…

A: use the intermediate value theorem and Roll's theorem to show that the eqautionx2=sinx+1has a…

Q: If the inequality 1 - <1- sin [æ³y³[ < P ) |z*y*| for all æ and y. Then, find the lìm(z,9)→(0,0) 2…

A: We will use Squeeze theorem in the given problem.

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

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Q: Match the following guess solutions yp for the method of undetermined coefficients with the…

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Q: 5. If z = f(x, y), where x = r cos 0 and r sin 0, find z and and hence show that: (). (-(( 2 2 dz dz…

A: To find the partial derivatives of the following function in two variables by chain rule.

Q: [5] Use the Gaussian quadrature to approximate the integral 1 x²e¬*dx. (a) Choose n = (b) Choose n =…

A: As per instruction we are allowed to answer only two sub questions. The generalised Gaussian…

Q: If a, b, c, and d are constants such that .2 ax + sin bx + sin cx + sin dx lim 8 %3D 3x2 + 5x + 7x°…

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

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Q: show that the Pio Diophant ine equation 2x -5y= | has no integer Selutions .

A: Given, 2x²=1+5y² Here 5y2 is a multiple of 5 ending in digit 5 or 0. 2x2 can end in 1 or 6 But no…

Q: The integral / 2' )cos(2*) dx takes the form k cosu du when u=2* and f (x) =x- 5. What is the value…

A: we use the formula ddx(ax)=ax lna

Q: Given f(x,y,z) = sin (2xy) + 5xyz3. Find fyzy(3,2,4).

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Q: 2-If w(x, t) = Sin(x - + 3t) + Cos(2x+ 6t), prove that wtt = 9wxx %3D %3D

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Q: 16. Find he exact soution on The interval [0,2m] 25in?x ャ Bsinx +3= 0 5sinx t

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Q: ,In sec2(sin2y)dy can be evaluated by writing it as sec2y (A @ In sec2( sin2y) · cos2ydy ®/…

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Q: Please see the attached problem. Thanks!

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Q: . If 4=(x+2y+az, bx-3y-z,4x+cy+22) is irrotational. Find constant a,b,

A: Follow the procedure given below.

Q: Show that the quen dffecential equation is not exact hance given Solve it Ky de (x'ay) dy

A: To show : The given differential equation is not exact then solve it. Given information: The…

Q: If f(x) = 12sin(green wave), then the red wave isi %3D 20 |-3T/2 -TT T/2 TT 3h/2 2n |-10 IF f(X)=12…

A: Red wave satisfies the point -π2,0,3π2,0  a) Given,   6sinx+π+6 Put x=-π2…

Q: 5-Vx+25 limr→0

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Q: .2π π 1 -εrocos? θ r dr sinθdθ φdφ x 32 πο X = ?

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Q: 10. If e is the acute angle between the surfaces xyz = 3x + and 3x - y + 2z = 1 at the point (1 -2…

A: We have to solve given problem:

Q: 6. If x= sect and y=tant, evaluate at t =- of the following: dy (a) dx d'y (b) dx?

A: x = sect y = tant

Q: 5) why is x3- 3x +I X +2 Conti nuous (0,00) on where is it discontinuous?

A: