Find the coordinates of the points where the gradient is zero on the curve y = x + . Establish whether these points are local minimum points are local maximum points.

Q: p and 4 ave selan function, and cs constant, Pmve that,

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Q: Consider the matrix A = | 0 2 (1 1 1 (a) Compute the determinant of A by expanding along the second ...

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Q: Answer C only

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Q: fT: R? → R* is a linear transformation such that 13 7 () - 26 and T then the standard matrix of T is...

A: Introduction: Every linear transformation from a vector space to another vector space has a matrix r...

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A: Given function is hx=6x3+7x2−16x−12

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A: Given  2ydx + (3y - 2x)dy = 0

Q: 4.14 A rectangular arrangement of numbers or terms having various uses such as transforming coordina...

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Q: b) det(AB"A') = det B %3D

A: We have to prove or disprove the equation detABTA-1=detB, where A and B are square matrices. We know...

Q: n=1 ) Let a, = In(2n +1) – In(2n – 1). Does {an}1 converge or diverge? ) Let SN be the Nth partial s...

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Q: Consider the following system of four equations. You are given two solutions X1 and X2. Generate fou...

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Q: 3 If the characteristic roots of 2 7 are A1 and A, the characteristic root of 7 are - 2 3

A: Given matrix is 3725 with λ1 and λ2 its eigen values.

Q: Determine the values of k such that the system of linear equations does not have a unique solution. ...

A: Given x + y + kz = 3 x + ky + z = 6 kx + y + z = 6

Q: The approximation of the solution x*of the equation x2 In(x+ 1)-x- 2 0 accurate o within 10 ² using ...

A: Here given equation is x2ln(x+1) - x - 2 = 0Let  f(x) = x2ln(x+1) - x - 2

Q: 2. y" + 4y' + 5y = 35e**, y(0) = -3, y'(0) = 1

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Q: Find the unknown variable: 10Cr = 252

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Q: /hat is the value of p if the solution of the given near equations has infinitely many solutions Оа ...

A: System of Linear equations and infinitely many solutions

Q: Problem 3. Solve the following simultaneous equations using determinants: 3x – 4y = 12 7x +5y = 6.5

A: Given system of equation is  3x−4y=127x+5y=6.5......1 We have to find the solution of the given syst...

Q: 3. Consider two vectors v = and w =. (a) Decide if v and w are linearly independent. (b) Decide if i...

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Q: A unitary matrix is deemed a unitary matrix when it has with complex entries and if Al=A", where A'i...

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Q: The results of a certain medical test are normally distributed with a mean of 130 and a standard dev...

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Q: Consider the following system of four equations. You are given two solutions X1 and X2. Generate fou...

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Q: Now that we have figured out how to do step 1, we are going to try and do steps 1 and 2. Given the d...

A: Given differential equation is y'' + 5y' + 3y = 0, with y(0) = 1, y'(0) = 0

Q: (b) Consider the following vectors u, v, w, and z u = [9.3 1.6 -0.9], v = [-7.8 5.9 5.3], w = [5.1 0...

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Q: (Final) Given the function f(x)= (Inx)*, find numerically, to three decimals accuracy, the value of ...

A: To determine the root of the equation fx=0, use the following Regula falsi method formula. xn+1=xn-1...

Q: Vx E R, Jy E R, x + y = 0 %3D

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Q: On the decibel scale, the loudness of a sound, D, in decibels, is given by D= 10 log (1/1,), where l...

A: D=10(logI-logI0)=10logII0 Where I= intensity of the sound in watts per square meters I0=intensity of...

Q: dy dx3 y (0) y' (0) 1 y" (0) = 0 || ||

A: Introduction: The differential equation of the form D3+aD2+bD+cy=fx is third-order linear on-homogen...

Q: Use the figures below to answer the questions: n = 1 n = 2 n = 3 Type the value in the box that repr...

A: We will construct the sequence with first three terms and will find out its recurrence relation.  

Q: a az 3. In R, let Wbe the subset of all vectors v = that satisfy a, -a, = a, – a,. az a4 a) Show tha...

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Q: 1. Where does the graph of y = x“ + 4x – 1 have horizontal tangent? %3D - 2. Use the chain ule findd...

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next ...

Q: If you bought thirty, 12 packs of soda for a party and you had 180 guests at your party, how many so...

A: Introduction: In arithmetic, we use the unitary method in solving various problems. This method invo...

Q: 6. Consider the subset S of R², S = {(x, y) | x – y = 1}. Decide if S is a subspace of R?.

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Q: (9) Suppose that ) An is a series so that its partial sums Sk = a1 + a2 + ...+ ak satisfies n=1 1 1...

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Q: 3. Let fx) --2x (x² - 9)(x*-1) Determine

A: Please find attachment for the details solution

Q: L( -1 2 s2-2s+9

A: We have to compute the inverse Laplace transform of the function fs=2s2-2s+9. We have to use the pro...

Q: Which among the following statements is true? * Every conditional statement is logically equivalent ...

A: Given the following statements I) every conditional statement is logically equivalent to its convers...

Q: For the given surface f (x, y) = 2 + sin(xy) at the point (1, 0, 2), find the following: a) Gradient...

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Q: Suppose f : (a, b) R is continuous at every point in the open Question 3 interval (a, b), and that f...

A: Introduction: Continuity is an important property of a real-valued function. A function is continuou...

Q: L{2t5 e5t } =

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Q: 1. Find the roots/s using Secant Method a) x - x - 10 = 0 4. Ans. x = %3D

A: Please find attachment for the details solution 

Q: (c) Find the chromatic polynomial of the graph in Figure 4. Figure 4:

A: Chromatic number of the graph

Q: Let S be the solid obtained by rotating the region shown in the figure about the y-axis. (Assume a =...

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Q: Determine the quadratic equation that best fits the given set of data: (1, 2), (2, 3), (4, 3), (6, 4...

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Q: In a gathering, the host makes sure that each guest shakes hands with everyone else. If there are 30...

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Q: Evaluate : 12C5

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Q: Let p and q be propositions. Then p →1 19 A(p → q)] is a

A: we find this by using truth table.

Q: Find the area of the plane region bounded by the curves y = √x − 1, y = 3, the x-axis, and the y-axi...

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Q: In the Philippine 6/42 lotto, a bet consists of choosing any 6 numbers in no particular order from 1...

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Q: Use the Laplace transform to solve the initial value problem below. y" – 22y' + 121y = t, y(0) = 0, ...

A: Given differential equation is y'' - 22y' + 121y = t with y(0) = 0 ,  y'(0) = 1