Let f(x, y, z) = -2xy − xz + 3yz + 1⁄x² + 3y² + z². - The set of critical points of f is

Q: Ва ut = Zuxx – ucot )=32 т и (ч, t ) = 52 та heat equation Ic = 4 (xio)= 5x+2 осхи

A: Using separation of variables method

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A: Given the function f is                f(x, y)=9y2e6x,  3, 1

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Q: 37. A helicopter at point T is 200 meters above the sea MN. If the angles of depression of boat Mis…

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Q: 2. Suppose that {f(t)} = F(s) with F a differentiable function and that {f(t)} exists. Then L{-te*…

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Q: 1.2. In the process of calculating L-¹ given by: -2.L -2s +3 we get an equivalent expression 10s 7 ^…

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Q: 4. Express each of these statements using predicates, quantifiers, logical connectives, and…

A: The given statement is  "The product of two negative integer is positive."

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Q: Determine the dimension of the span of each set. 6 3 12 - A = span ({0}) 2 - -1 4 20 10 40 dim (A) =…

A: Follow the steps.

Q: Solve y" -8y' +16y = 0

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Q: Converting from...... to....., include divide by two, to keep track of the remainder O Decimal to…

A: Follow the steps.

Q: aplace transform, solve the IVP. = 5y₁ - 4y2-9t² + 2t, y2 = 10y1 - 7y2 - 17t² - 2t, _0) = 3, y₂(0) =…

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Q: 1. Show that a frination fiłamb ]->1R is differentiable at xolamb) is and only if its lower and…

A: Solution:f:[a,b]→ℝ is differentiable at x0(a,b)Let us take upper derivative at x0+then…

Q: 6. A bacteria is known to double every 20 minutes. How long will it take 5mg of bacteria to grow to…

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Q: 1. Complete the chart below, converting between logarithmic to exponential form. Logarithmic Form…

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Q: π/2 1- ²₁/²(y² sinx dx dy) dx 2-52²2 ₂22 22 0 x²+2 3- f(cscx cot x)² 4- f₁²³ x (x − 3) dx 5- f₁² (x³…

A: According to the guidelines ,we can only solve 1 question or 3 sub parts . I solve question numbers…

Q: 12. Consider the function f, such that f and f' are continuous for t≥ 0, defined by 37t - 95 0≤t<7…

A: Also given  f'(t)=37+(4t-28)u(t-7). We find the value of b.

Q: dy = f(y). dt The following problem involves an equation of the form Sketch the graph of f(y) versus…

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Q: Task 2: Calculate the volume under the surface z = 3+x²-2y over the region R defined by 0≤x≤1, -x≤ y…

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Q: Without appealing to Heine-Borel, prove that [0, 1] CR is compact and connected in the standard…

A: Please check in the next step

Q: A hole of radius 3 is bored through the center of a sphere of radius 5. Let the cross- section of…

A: we will draw region which can be rotated to create solid region whise volume needed to find . Then…

Q: Answer the following: 1. Evaluate: 00 e³z 1 = (e* + esz)z dz

A: Given: I=∫0∞e3zez+e5z2dz To find: Evaluate the given integral.

Q: b)* Describe the set {TER²: doo (1, (0, 0)) = 1}.

A: We have to describe the given set x∈ℝ2 : d∞x, 0, 0 = 1.

Q: find the radius of convergence for this taylor series expansion in 30 minutes and get the thumbs up

A: Radius of convergence of the series

Q: Find the directions of maximum and minimum change of fat the given point, and the values of the…

A: Directions of maximum and minimum change of f

Q: y Find Laplace tras Function sform of The following 644 -3t B) f · (t) = @²² (f+m)² where M is a…

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Q: 4. Given vectors: =(4,9), v = (-8, 15) and w=(2, 10) a) Show that and w can span R².

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Q: 1.047i 4Q. Using De Movier's Theorem find all roots of √/25 e¹

A: The given problem is to find the all roots the given complex expression by using De Movier's…

Q: 11. Determine the solution of Utt = u (x,0) = 0, u (0, t) = h, where h, k, and A are constants. c²ur…

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Q: Exercise : Let f be a power series centered at the origin. Prove that f has a power series expansion…

A: Given that  f=∑n≥0 anzn for an∈ℂ and say it convergence for values z∈ℂ such that z&lt;R. Take z0…

Q: If A = i-2j-2k, B = 6i +3j + 2k, find A.B if 0 = 70 7.182 4.897 O 12.5 O 5.12 O

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Q: 4. Consider the convolution f(t) = 24 2(t-11), where corresponds to the Heaviside or unit step…

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Q: 3.. cos(x) is not an odd function O True O False

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: Solution of the differential equation

Q: (b) Find the Inverse Laplace transform of the function. G (s) s-7 s² + s-6 =

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Q: Fit the following variables with the formula: Y = a ex X₁ 1 2 3 5 6 Y₁ 1.3 3.5 5.0 7.0 8.8 4.2

A: The given problem is to find the best fit curve for the given data by using least squares method.…

Q: Obtain the roots of the following equation by the fixed point method starting at x = 1 and solving…

A: To obtain the root of 4x2-2x-9=0 using fixed point method with x0=1

Q: Which of the following is a solution to the differential equation (r+sin Ө - cos Ө)dr+r(sin Ө + cos…

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Q: 3.. cos(x) is not an odd function O True O False

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Q: Which of the following sinusoidal equations has an amplitude of 9, a period of 1080 and a maximum at…

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Q: 5. lim,- A.7 A D B 7x²+x-100 2x²-5x B 7|N C. / D.2

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Q: Find the four roots of ( 3 + i4 )

A: We know that , Complex number is of the form , z = x + iy. Also , Polar form of complex number is…

Q: 14- 2x (x-4) (x-1) dx =

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Q: Q3. Prove by using logical equivalence method: (pr) V (q+r) = (p Aq) → r

A: Two propositions are referred to as logically equivalent if their truth value is always same. When…

Q: Consider the following propositions associated with the study of the +∞ dx J - 1.1² √6 +1 improper…

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Q: 2. Use the method of equation Uariation of parameters to solve the differential dy - k- dx² dx xez…

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Q: (x, y) = x + sin(y²x) 2y y #0 y = 0

A: Given function f(x,y) =x+siny2x2y,  y≠0x,                      y=0 fx0,0=limh→0 f(h,0)-f(0,0)h…

Q: State the order of the given ordinary differential equation. (1-x)y" - 9xy' + 2y = cos x Determine…

A: Order of the differential Equation :  The highest order of the differential Equation is called the…

Q: piz 9. Find inverse Laplace: | es S

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Q: f: X → Y be a surjective function. Define a relation on X by setting ay iff f(x) = f(y). Show that…

A: Please check the solution in next step