Determine all the relative minimum and maximum values, and saddle points of the function h defined by 3 h(x, y) = x³. 3x + 3xy²

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Q: Suppose f and g are two functions with nonnegative values. If f(n) is (n) and g(n) is (n³/2), then…

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Q: Consider the spherical equation given by p = 4 cos sino. Determine its corre- sponding equation in…

A: The relation between the spherical co-ordinate and cartesian coordinate are  x=ρcosθsinϕy=ρ…

Q: 1 u = ----- (1, 1, 1, 0), V 3 1 -- (-1,-1, 2, 0) W = V 6 1 - (1,-1, 0, 0) V2

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Q: Find the Laplace transform of the following: 1. f(t) = 5t²u,(t) + 3(t – 4)³u8(t) — 9 sin ( - ) u₁(t)…

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Q: 2. A=?, B = 76° 48'

A: Sum of angles of a triangle =180° Using this third angle A can be founded.

Q: The face of a vertical dam has the shape of an isosceles triangle of altitude 4 m with an upper base…

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A: The given graph is

Q: Q. 8.(a) Let {e} be an orthonormal set in a Hilbert space H, then Σ|(x,e₁) | ² ≤ |x|² for each…

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Q: A rectangular box has sides of length x cm, y cm and z cm. Sides x and z are expanding at rates of 3…

A: This is a problem of the application of derivative.

Q: Use Laplace transform to solve the partial differential equation: d²u du = t> 0, 0<x<1, u(x,0) = sin…

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Q: 3 x = y + z- w = 2 -x + 2y - z - w = -1 2x - y - z+ w = 4 x + 3y - 2z - 3w = 6

A: 3

Q: Differentiate x²y3 - y2-6x=0 with respect tox. A 3x²y2-2y −6+2ху 3 2х3у2-2y - 6 6-2xy3 3ху2+у В С D…

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Q: Determine the most suitable guess value, r to select for x", if given the differential equation such…

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Q: Determine the time required for the bacteria concentration to be reduced to 5 using Newton's method.…

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Q: Which one of the followings represents the ceiling of X? o[x] olxl o [x] o [x]

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Q: What is the sum 1+2+4+8+...+512?

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Q: Discount ₱15,800 for 11 months at 14.25%simple interest.

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Q: For the parametric surface r(u, v) = (u cos v, u sin v, 0) where 0 ≤ ≤2 and 0 ≤ ≤ 27 and which is…

A: Given r(u,v)=u cosv, u sinv, 0 where 0≤u≤2,  0≤v≤2π r→u=cosv, sinv, 0 r→v=-u sinv, u cosv, 0…

Q: Region bounded by y2=16x, y=8, x=0. Region is revolve about the y axis. Find the volume using disk…

A: We have to find the volume of the region bounded by the the curve y2=16x, y=8 and x=0 revolved about…

Q: If R is the disc with center at the origin and radius 5 then the numerical value of Lxds R xdA is…

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Q: Show that the function g defined by YVT g(x, y) = y² + √√x²¹ 2, is not continuous at (0, 0). = (x,…

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Q: A manufacturer is planning to sell a total of 300 machines to both foreign and domestic firms. The…

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Q: 4. y' + 2y" - 11y' - 12y = 11t -9, y(0) = 0, y'(0) = 0, y" (0) = -3

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Q: The power series representation of f (x) = ln(x2 – 1) is given – Ο A. None of the choices in this…

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Q: Find the first derivative (i.e., general solution) then solve for the particular solution using 2nd…

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Q: Consider the region on the 1st quadrant bounded by y = √4x²,x and y - axes. If the region is…

A: Introduction: A stable of revolution is a stable parent created with the aid of using rotating a…

Q: 1 u=-----(1, 1, 1, 0), V 3 1 -- (-1,-1, 2, 0) W = V6 1 =(1,-1, 0, 0) V 2

A: Here we have to determine whether or not the following set of vectors { u, v, w } are both…

Q: Consider the spherical equation given by p = 4 cos sino. Determine its corre- sponding equation in…

A: Since the relation between the spherical coordinate and Cartesian coordinate…

Q: create 2 sample word problems that has derivative formulas with solutions

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Q: Find the first derivative (i.e., general solution) then solve for the particular solution using 2nd…

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. The x-coordinate of the centroid of the…

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Q: Example 2.40. Solve x¹-5x³+20x² 40x+60=0, given that all the roots of f(x) = 0 are complex, by using…

A: Here we need to solve equations using Lin-Bairstow Method.

Q: create 2 sample word problems of integral leading to exponential and logarithmic functions with…

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Q: 1. y=x²-1, y=-x+2, x=0, x=1

A: To find the area bounded by each of the given curves :-

Q: 8 The interval of convergence of the series (√n+1-√√n)(x+2)" is given by n=0 OA.-3<x≤ - I.…

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Q: Evaluate the following definite integrals. Note: Final answer should be expressed as a decimal, not…

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Q: Using False Position Method, what is the root? Use error = 1 x 10^-6

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Q: 4. Which of the following vertices are adjacent to vertex B? B E F OA) AEDC OB) AEFC OC) AEDFC OD)…

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Q: group. (b) What do you mean by conjugate elements and classes ? Find the classes of the (Rohilkhand…

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Q: QUESTION 3 Let f= (17624) and g = (15632 7) be permutations in S7, written in cycle notation. What…

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Q: Find the Laplace transform of the following: t, 2. g(t)= (t-4)², (9t-e20-4t, t<3 3<t<5 t≥5

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Q: Solve for the order of each of the following: a. 1-i√3 under usual multiplication b. 5 in Zs under…

A: "Since you have posted a question with multisubparts, we will solve the first three subpart for you.…

Q: Choose any that is an arithmetic series. 4+8+12+16+...+200 50 Σ(1-2) j=5 45 Σ(12 + 3) j=1 45 Σ 3* K…

A: Here we have to choose the arithmetic series. A series is said to be arithmetic series if difference…

Q: (e) Let V = Mat2x2(C). A linear transformation T: V → V is defined by a b -a 7[:] [74] d]. T: Find…

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Q: 5. Solve y" - 3y + 2y = 2et, y(0) = 2, y'(0) = -1 a. et + 4et-e²t b. et + 4e²e²t - et + 4et-e²t d.…

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Q: y" — y' — 6y = t²e³t — 4t², y(0) = 0, y' (0) = -1

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Q: Determine the value of k for which Assume that k is a positive number. k 4 2k k 1 = 0

A: Let us considre a 2 x 2 matrix A=abcd The determinant of the matrix is obtained as |A|=abcd=ad-bc A…