. (a) Solve the boundary value problem Ju + Be-12 at where u(0, t) = 0, u(L, t) = 0, u(x,0) = f(x), u(x, t)

Q: 6. For what values of y(0) will the solution of y' = y(y – 2),x > 0 a) be a constant function b) be…

A: First of all we draw the direction field of the differential equation y' = y(y-2)

Q: Let f(x, y) = x2 – y?. Find (a) The directional derivative of f at (-2, 1) in the direction of v = i…

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Q: 2. Let closed curve C consist of the line segment from (0,0) to (2, 1), followed by the line segment…

A: We will solve both the parts using the basics of integral calculus, in particular double integral,…

Q: The Domain of f (x) = V1 – x is 1. [-1, 0) 2. (-∞, 1] 3. (-0, 1) 4. [1, c0)

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Q: Suppose z = x + iy and f(z) = z - 1. Find w = u + iv such that f(w) = 1 + 3i (A) 3+2i (B) 3-2i (C)…

A: We have given that , fz = z - 1 , where , z = x + iy Here , w = u + iv Let , fw = 1 + 3i We need to…

Q: f(x,y) be defined implicitly as a function of x and y by the 3xyz =exyz Əz Əz yay ax Əz Əz Find and…

A:

Q: length, is given by the heat equation, ди 2²u əx² Ət (0 0), here x measures distance along the bar,…

A:

Q: Which of the following most accurately de- scribes the behaviour of f. 1. local maximum at (2, 0) 2.…

A:

Q: f(x, y) = xy(3-a-y) OA. (1, В. О в. (0, 1) O C. (0,0) O P. (-3,3)

A: Given function is f(x,y)=xy(3-x-y) At first we differentiate it partially w.r.t. x and y and setting…

Q: (12 Use differentials to est imate fl-2.01) it fCx): x/T-x.

A: We need to find differential estimate. NOTE- As per Bartleby's guidelines we can only solve one…

Q: f(r, y, z) = sec='(9x + 3yz) f. = fy = f; =

A:

Q: Q4 A) Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

A: The objective of the question is to verify the hypothesis of the Cauchy Picard theorem for the given…

Q: 5 of 9 > Let f(x, y, z) = 5x³ · y³ + z². Find the maximum value M for the directional derivative at…

A:

Q: 4. xyzx + 2y³ (2)³ = 1 Dependent variable/s: Independent variable/s: Type: Order: Degree: Linearity:

A: Solution :  To discuss about the nature of given differential equations

Q: Find the maximum value of f(x1,2,,xn) = (x₁ - x₂ ... n)¹/" where x₁,..., In are positive numbers and…

A: (a) Maximize?(?1,?2,...,??)=?1?2...??n subject tog(x1,x2,...,xn)=x1+x2+.........+xn=cand xi>0By…

Q: (b) Let z(r, y) = exp(-|r|) cos r + y², where r + y /9 = 1. Show that z(r, y) has minimum points…

A:

Q: Find the equation of the tangent plane to f(x, y)= x´ – x y – y at point P (1, 1, -1).

A: Consider the equation

Q: Let f(x, y) = x³ + 2ry – y² be a func the tangent plane to f(x, y) at the poi

A: Here we have f(x,y)=x3+2xy-y2  we have to find the equation of the tangent plane to f(x,y) at point…

Q: Consider the following function: H(x, y) 7x'y +-21x'y Find the linear approximation of H(x, y)…

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Q: Transform the function y=(1)/(2)x right 6 and vertical shrink of (1)/(4)

A: The given function is y=12x. To transform the function rightwards by 6 units and to shrink…

Q: efined by. Hn(X) +h. iu

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Q: 1 4) S(x, y) = Ans. f(0,0) = -1 local max. x+y -1

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Q: The equations ry?+ 5zzcos(u) + ye" = 10 and r*yz+xe" – 10u²v² = 30 are solved for u and v as…

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Q: Show all work! Find the maximum, minimum, and saddle point of f(x,y) = cos(x)+ (1/y^2 + 1/x)+1

A: We will use the basic knowledge of 2-variable calculus to answer this question.