2. Show that any bounded harmonic function in R" is constant. Hint: Use the fact that if u is harmonic, then so is u,, i = 1, 2, ..., n. %3D Solution:

Q: he characteristic curves for the IVP u+4 u,+2 u 0; (x, 0) = sin x; - 00 C are O a. T= X-t . T=X- 8…

A:

Q: The function yow) satisfies the differantial equation x dy + ay Cos(xx) ak y(1) = 1 , the valu of…

A: Given differential equation is  xdydx+2y=cos(πx)x,y(1)=1

Q: at is the Ar+B drif A=0 and B 12+1 25 arctan (r2 +1) +c 25 0- Arctan x +c 25 o In |z² + 1| + C 25 25

A: Put value of A and B and then solve

Q: a) Use the definition of the hyperbolic functions to prove that 2cosh?(x)–1=cosh(2x). 1%3D

A:

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: b) Now, we will assume that f(x, y, z) is a harmonic function. Show that ·ds

A:

Q: 2. STO Find the length of the graph of y = 2+ In(sin z) om the interval [7/4, 7 /2].

A:

Q: 3. Let G = {z = x+iy : x < 0 or y # e" sin x}. Show that G is simply connected.

A: Given: G=z=x+iy; x&lt;0 or y is not equal to ex sin x

Q: and casy=0t, and DLyr, Furd the exact alue of tan Ca-y.

A:

Q: f arctan y dy 3 ¥

A: Given problem:- ∫arctan(y)/y3 dy

Q: The function f(x) satisfies the hypotheses of the Mean Value Theorem on %3D cos(z)+1 Select one: a.…

A:

Q: Q4: (a). Prove that u = 2x(1-y) is harmonic.

A:

Q: is stricly increasing on (0, T /2). sin x Prove that the function f(x)=

A: Given that: f(x)=xsinx

Q: let Po)- tar'c) + tant (L). show that Plx)=C,where cis a constant and then Aind C

A:

Q: 1. Integrate the following functions over the given interval by using the extended trapezoidal rule…

A:

Q: Let z be defined implicitly as a function of r and y by the equation əz 4+ In (ry²) - cos (xy - z) =…

A:

Q: Having f (x) = 1 +e¬* sin(4x) and the interval [0,1] Apply composite Trapezoidal and Simpson's rules…

A: I have done by the direct method and trapezoidal rule and find the error by trapezoidal rule

Q: az dz Find the and of the following function; ax ду (а)z %3D xln(ху) + уз, у3 сos(x? + 1) (b) z =…

A:

Q: Let f(x) = In(cos(x)). For what value of c is f'l =CX + TC 1? 4. C =

A: We can solve it for the value of c as below

Q: h(z) = e sin z – sin z + cos z

A: This problem based on application of derivative.

Q: Let u > 0 be harmonic in R². Show that u is a constant.

A:

Q: (a) Find a harmonic function u on the upper half-plane that has the following boundary values. (1…

A: Detailed explanation mentioned below

Q: 6- What is the arclength of the function y = 7x + 2 on the interval [2,6]? a) O /2 90406 b) O 20 c)…

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Q: f(z) = cos-1 (포) -er s=(z) – e²

A: Concept of IVT is used while solving this problem.

Q: ind c, and c2 so that y(x) = c, sin x+ c2 cos x will satisfy the given conditions. Determine whether…

A:

Q: Determine the largest interval in which the unique solution of (t - 3)y +tan ty = t, y(n) = 0 is…

A:

Q: The approximation of I = , tanx dx using composite Simpson's rule with n-5 is: None of the choices O…

A: f(x) = tanx Each interval h=(b-a)/n =1-0/5=1/5 =0.2 xO=0, x1 =1/5, x2=2/5, x3=3/5,x4=4/5, x5=1…

Q: 학과 학번 Determine the value(s) of d satisfying that Lacos(br+c) + d de lim 2-0c tan r dr for any real…

A: Integrate as follows.

Q: 8. Verify that the function u(x, y) = eª sin(y) is harmonic in the region where it is defined and…

A:

Q: Find the largest interval on which the following IVP has a unique solution. (2t + 1)y" + sin t y…

A: NOTE: Refresh your page if you can't see any equations. . to find the undefined point take…

Q: Which of the following statements are true? Ly=coshx is an odd function. I. y=sinhx is symmetric…

A:

Q: Let C be the shortest path that connects a to ni and I = fe (sinhz + 1)dz. Then None of these…

A:

Q: 3. For what value(s) of r on [0, 7] is the line tangent to the graph of f(x)= cos z horizontal? %3D

A:

Q: Let z be defined implicitly as a function of r and y by the equation dz 4+ In (xy?) – cos (xy – z) =…

A: We know that (u·v)' = u·v' + v·u' ddxtanh-1x = 11-x2 ddxfu(x) = dfdu·dudx      (chain rule)   Given…

Q: -8. AB is tangent to to OC at point B. E 6. MZCDA - 8. MZDBA = 32

A:

Q: In the case when U = x on the edge y = a (where Yo is a constant), a calculate C, inorder to show…

A: Given at y=a, U=ψ0ax     …Equation(1). And, on substitution of y=a in expression…

Q: S-) Find the gereral solufon of Sin'x y"- (2sinx.cos x)g'+ Ccosx+1)y = Sih? x given that y-sihx and…

A: Given differential equation is sin2xy"-2sinxcosxy'+cos2x+1y=sin3x Here, qx=sin3x Given that y1=sinx…

Q: If u(x, y)= In(x² +y² ), then examine that whether u(x, y) is harmonic or not. If u (x, y) is…

A: The partial derivative of a multivariable function with respect to a variable is the derivative of a…

Q: lim, ,0* Sõ sin(t*) =? O a. 00 O b. 1/3 O.c0 O d. 2/3 O e. Limit does not exist е.

A: The correct option is, option (b), i.e. 1/3 The detailed solution is as follows below:

Q: 2, If fCx)=xInCx²+), find the ea uation for t4e tan9ent 1ine to fCx) at x= 3.Hint: Remember the…

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Q: Show all steps to verify that fry = fyx given f(x, y) = cos(2x) – x²e5y + 3y²

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Q: 4) Given: AB is an external tangent to Q0 and 0Q at points A and B, radi for O0 nd OQ are and 12,…

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Q: Given f(x) = , 1+ cos²(t) t? - 9 dt %3D 0. At what value of x does the local max of f(x) occur?

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Q: Find the minimal period T of the function: f(x) = 5 cos (rx) + sin (rx). %3D Answer: T =

A:

Q: Find y' of the following function using MATLAB y = sec(In(2M * x))e5x + cos(2Nx)

A: here we write the function in MATLAB and then by using the command  we can find the derivative of a…

Q: 5. Find Oz дz дх and if x - z = arctan(yz) defines z implicitly as a function of x and y. ду

A:

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: b. Find y' of the following function using MATLAB y = sec(In(2M * x))e5x + cos(2Nx)

A:

Q: Let f (x) = In (x?) find the equati on oE the line tangent to the graphof f at (3, In(9)) (2) Find…

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Q: please solve this question

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.