Find out all the relative minimum and maximum values, and saddle points of the function h defined by h(x, y) = x³ – 3x + 3xy? -

Q: 1- Use Euler Method to find value of y at x = 1.5 for the D.E. y' = x/y with initial value y(o) =…

A: We first find the solution by Euler method using the step size h=0.3 of the given differential…

Q: (-0.1)-금 (30)+ (150) f-0.1)= 2 3. (-0.1) 3(-0.1) -0.)(120)=683 6. 4

A: Here we have to go back to just previous step were we have function,…

Q: Find the general & particular solution of the DE, 4y" - 16 dy/dx + 16y = 0 with the given that y(0)…

A: The solution is given below.

Q: A certain animal population grows continuously. In 2013, it was recorded that the population was…

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Q: f(x) = tan¬1(2x²) – 1

A: Newton's Raphson Method:- Hence Positive root of given equation by NRM is 0.88244

Q: 1 3 5. -2 ? Why? 5. -2 2 B = 3 -1

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Q: 5. Solve by finding series solutions about x=D0: (x - 3)y" + 2y' +y = 0

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Q: Let V = R be the set of positive real numbers. We define addition and multiplication with standard…

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Q: 3. Let n > 1 be an integer, and let J : Pn → Pn+1 be the indefinite integration transformation on…

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Q: Duse the Runge-Kutta Method Solve the: Say tanrs tan x-Sinz X, ylo)=1 ,h2 0.1

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Q: The value of a certain photocopying machine t years after it was purchased is defined by P(t) =…

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Q: A certain college graduate borrows 8391 dollars to buy a car. The lender charges interest at an…

A: given Bt=8391 at t=0 rate of interest τ=13%   =0.13 payment rate =k at time 7 years  B7=0 now,…

Q: 1241 + 245x2 + 35x3 + 24x4 = 24 %3D 356x + 24x2 + 35x3 + 75a4 = 2 24x1 + 56x2 + 35x3 + 67x4 = 47…

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Q: Find the general solution for the following differential equations: (a) (1 – xy + x²y²) dx + (xy³ –…

A: As per policy, we are allowed to answer only one question at a time. So, I am answering the second…

Q: A criterion that when a candidate wins an election, and a re-election is held in which the only…

A: Correct answer is monotonocity criterion.

Q: :Write step by step solutions and justify your answers. Ques Evaluate L fe³ – (5t – 2)² - sin(-5t) +…

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Q: ne number of bacteria B(t) in a petri dish culture aftert hours is ven by B(t) = 400e0.876t When…

A: Population of bacteria

Q: Prove that l17 is the only prime number of the form n²- 64.

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Q: Let A be a diagonalizable matrix, with characteristic polynomial det(AI – A) = (A – c)" for some…

A: Diagonalization of the matrix

Q: (c) Let M be the surface with the equation r³ +y³ +z = 9 that is above the right triangular region…

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Q: 1.) Bacteria multiplies in a rate in which a bacteria splits into two new cells, thus doubling its…

A: a. The number of bacteria is calculated by using the following relation. B=2t where B represents the…

Q: 2) Consider a bicyclist whose position s(t), in feet, is given by the table where t is in seconds. t…

A: The velocity of bicycle is represented by the derivative of st with respect to t.

Q: Summing Series (numeric summation): Tylor Series: x2 x3 x4 M -1- x+ e-X = 2! 3! ..... 4! 5! n=0…

A: We have to find the exact exponent and sum of series upto that terms.

Q: What is true about using the local linearization, L(x), for a function f(x) at x-a ? Select all that…

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Q: 1. Verify Green's theorem in the plane for $ (3x2- 8y,dx + (4y - 6xy)dy, where C is the boundary of…

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Q: 1. (D² – 2D – 3)y= 64xe³x

A: To solve the given differential equation.

Q: we have 1529 MOD 83 = 2 Find the inverse to 2 by using the Euclid's algorithm

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Q: Advanced Math A company estimates that the production cost function of x product is giving the…

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Q: The measure of the linear density at a point of a rod varies directly as the third power of the…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

Q: 2. Find the Fourier series expansion of: So, sin Tz, 0<r<1 -1<1<0 f(r) = and then use it to find the…

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Q: 1. Provide any set S1 and S2 such that: (a) Si and S2 are subspaces of R", and that (b) Si U S2 is…

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Q: 5. Consider the double integral rydA r=4+4 cos(0) = 25 Where R is the region of the XY plane, i1 -io…

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Q: · (D³ - 3D² - D + 3)y = 0

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Q: Show that the equation Əy + 2k Əx? possesses solutions of the form 00 2 c, e-kt 1" =0 Σ cos (a, x +…

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Q: 2. At what point on the line y = b does the line segment from (0,0) to ( a,0) subtend the greatest…

A: at what point on the line y=b does the line segment from 0,0 to a,0 subtend the greatest angle.

Q: Find the value of x for which Inx + (Inx)2 + (Inx) + (Inx)* += 9

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Q: 1. a) Find a linear transformation L : R³ → R³ whose kernel is spanned by the set {{:) (}} S = 6)…

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Q: Express the double integral in terms of a single integral with respect to r. Then use a calculator…

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Q: The graph of a function f is given below. According to the graph, the derivative of the function…

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Q: ĐUse the fuler method's Solve the: 5.525ー0 ら10)=1 hこer

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Q: Tabular method for simultaneously summarizing the data for two categorical variables is called…

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Q: Evaluate F. dS, S where F(x, y, z) = (3xz – Vy? + 2?, sin(x – 2), e" - z²) and S is the surface…

A: Since S is the boundary of closed region in space. So we apply the Gauss Divergence Theorem.

Q: 2.4 If (x, y) = -r* - y" + 2ry – 8r" + 7y, , then in the process of obtaining its critical points…

A: Given a function f(x,y) = -x4-y3+2xy-8x2+7y   Also given the equation obtained during the process of…

Q: Determine if the sequence {an} converges or diverges. Find the limit L if the sequence converge. an…

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Q: 3. (D2 + 2D + 1)y = 0 ; when x = 0, y = 1, Dy = - 1.

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Q: Evaluate the following limit. 7 cos t+ -7 e-t-1 sin 2t -i- 2t lim k 7t 31 7 cos t+ -7 e-t-1 sin 2t…

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Q: 2) Find the o - Congugates ot; c) 5

A: 2. To Find: θ-conjugates of  (c) 54 (d) 1+2

Q: Let E be the region that lies inside the cylinderx²+y² = 64 and outside the cylinder (x - 4)2 +y2…

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Q: 4. Let B = {v1, v2, v3} and C = {w1, w2, w3} be bases for R3, with vectors defined below. -(:) --()…

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Q: Prove that an angle of θ radians is constructible if and only if the real number cosθ(sinθ)…

A: Since θ is constructible, by definition, (cosθ, sinθ) is a constructible point.