2. Find the solution of Cauchy problem: (a) y lu, tuy = u, u(2,1) = ? (b) xux + yuy=x²-y, u(1,y) = y. (c) uz + 3uy = u², u(x,0) = h(r), where h(x) is a smooth function and not equal to zero.

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A: Variable line is                xa+yb=1                 ......(1)Any line perpendicular to (i) and…

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A: We will use parameterization to find line integral

Q: 3. Let f(x,y)=x²y/(x² + y²). (a) Show that f(x,y) goes to zero if (x,y) goes to (0,0) along any…

A: Solution: (a) If (x,y) approaches (0,0) along the straight line y = mx, then we can substitute mx…

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Q: 57) Given: f(x) = ax³ + bx² + cx+d, f(2)=5, ƒ"(1)=-4, ƒ"(4)=12 When x = 1 the tangent line to f(x)…

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Q: a) Suppose you are given model with two explanatory variables such that: Y₁ = a + B₁x₁i + B₂x₂₁x +…

A: Given: yi=α+β1x1i+β2x2ix+ui To find: Coefficients

Q: Find the maximum and minimum of f(x,y) = yx2 + y(y - 1)2 subject to x2 + y2 =1.

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Q: 58) Given: f(x) = ax³ + bx² + cx+d, f(1) = 5, ƒ"(-1)=-2, f"(x)=12 When x=0 the slope of the tangent…

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Q: 2) Given f(x) = ax²+bx+c has a y-intercept equal to 5, ƒ"(1)= 16, and (1,11) is a point on the…

A: f(x)=ax2+bx+cy intercept is 5f''(1)=16(1,11) is a point on the curve d dx(xn)=nxn-1

Q: If the time 26 + 1%/16 = 1 a that moves in such a way b 1/2 + 1/2 = 1/², where c is a constant, they…

A: Variable line is                xa+yb=1                 ......(1)Any line perpendicular to (i) and…

Q: a3 f 2- Find the third derivative for for f (x, y) = sin əx3 -2sin?cos()+2 sin) sin By'sini )+2…

A: The given function isf(x, y)=sinxy

Q: The equation of the tangent line for the function f(x) = -3 – 6x at r = 6 is %3D

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A: Since you have posted multiple question in this question which are nt interlinked so i have solved…

Q: 2 Sketch the level curve of the function f(x, y) = y - x² for c = -2,0,2.

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Q: 12. Findofy-7 a Find the gradient of the greph atos b) Show that the above graph has turning points…

A: Given-(a)-Equation y=x3-3x2+7...(1)Differentiate abive equation with respect to x we get that…

Q: - Find f (x) given f' (x) 6x2 - 4x + 3 and (2, 15) is on the curve of f (x) .

A: To find the function from derivative we need to integrate.Here we will integrate to find f

Q: . Show that each function is not analytic at any point but is differentiable along the indicated…

A: “Since you have posted multiple questions with multiple sub parts,we will provide the solution only…

Q: The equations ry² + 8xzcos(u) + ye® = 16 and x³yz + xe" – 5u²v² = 15 are solved for u and v as…

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Q: Let f(x) = 2x² 11a + 4 - The slope of the tangent line to the graph of f(x) at the point (2, 10) is…

A: This is a problem related to derivative of the function. Please follow the procedure given below.

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Q: In the xy-plane, the line tangent to the graph of 2 x² + xy + y² = 3 at the point (1, 1) has a slope…

A: Given equation is  x2+xy+y2=3  we need to find slope of the graph at (1,1)

Q: 4. Let f(x, y) = y³ +32²-6ry-9y-2, Find absolute maximum and minimum of this function on the…

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