4. The slope of a secant line represents the average rate of change.

Q: 25. (i) Calculate the determinant of thenxn matrix (1 1 1 ... 1 1\ 1 0 1 ... 1 1 1 1 0 1 1 ... A = 1…

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Q: M1 := sup ||T(x)|| and ||x||=1 M2 := inf{C > 0 : ||T(x)|| < C||x|| for all x e R"}. a) Prove that M1…

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Q: 3. The price-supply and price-demand equations of a certain product are given by p = S(x) = 15 +0.1x…

A: We will draw curves and identify area representing consumer and producer surplus . Then will find…

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Q: A company estimates that a certain piece of machinery will have to be replaced in five years' time…

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Q: I. For the following items, consider the function f(x,y) = 9x² +16y² А. Determine the domain and…

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Q: gener dx 1+2y? (6 marks)

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Q: 9. Consider the column vectors u and v in R" cos(0) cos(20) sin(0) sin(20) u = v = cos(n@) \…

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Q: Σ –3n \3n 2n+1 in=1

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Q: * dy/dx=(x+siny)/(2y-xcosy) is an exact equation false true

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Q: The graph of f(t) is given in the figure. Represent f(t) using a combination of Heaviside step…

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Q: Consider the stochastic matrix P = 2 1 1 3 4/x If q = 2/x is the stationary distribution of P, what…

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Q: 1. (i) Show that if A is an n x m matrix and if B is an m x n matrix, then A # 0 is an eigenvalue of…

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Q: . A rectangular tent is made to have a square base with two partitions inside that divide the tent…

A: We will find the function to be minimized and then use calculus to minimize it

Q: If 1 d 1 d a a det b = -1, and det 6 2 = 3, e e 1 f 3 f then a d det and e f d' det 1 e 2 f]

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Q: 4. The slope of a secant line represents the average rate of change. 5. When simplified,…

A: 4) True

Q: ĐUse the improved Method Sove the: 5.52ダー0 0-2

A: To find the solution of a given differential equation by improved Euler's method we will use the…

Q: Calculate the flow in the field F along the path C. F = (x - y) i - (x 2 + y 2) j; C is curve from…

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Q: Q2: Find a root of x - 0.5 – 2-2x = 0 by using Newton-Raphson method correct to %3D 4 decimals so…

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Q: 3) Find Possible Positive, Negative or Imaginary Zeros. f(x) = 2x³ - x² - 25 %3D Count the number of…

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Q: 4 a Evaluate In 3. b On the axes below, sketch the graph of y = Inx 3 2 -2 =3 The graph y = In x is…

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Q: FIND THE LENGTH OF THE CURVE 9y = x(x – 3)´ from X = 1 to x = 4 %3D 10

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Q: Q2: Find a root of x - 0.5 – 2-2x = 0 by using Newton-Raphson method correct to 4 decimals so that…

A: Solution :-

Q: Problem 10 (Hyperbolic Functions] (a) For what values of k is lime 3x cosh(kx) finite? X00 sin h(kx)…

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Q: Consider the function defned by f(X, y) = y-ex (a) Find the domain and ran ge of f. (b) Draw a conto…

A: If the graph of z=f(x,y) is sliced by a plane: z=c, then the two dimensional cross-section obtained…

Q: A man sold half an egg more than half his eggs. He then sold half an egg more than half his…

A: We can solve this by given information

Q: LINEAR DIOPHANTINE EQUATIONS 2) Determine the integral solutions for which x and y are positive. 2x…

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Q: Ex. Directions: Graph and describe each line given the following conditions. 2 through the points (–…

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Q: Approximate the following integral using the Trapezoidal rule: e+1 dx x In x and find a bound for…

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Q: 1 2 5 -2 - 1 -2 1 1 A= 4 4 V2 = V3 = 6 3 1 6 9 1 3. 3. 3. 2. 4. 2. 2.

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F = x 2y i  -…

A: To find the flux of the vector field F across the surface S. F=x2yi−zk S is the portion of the cone…

Q: Let B be the surface with equation x =-1+ /÷y. 24 (a) Provide a hand-drawn sketch of B. Label the…

A: As per the question we are given a 2d equation as : x = -1 + √(y/2) And we have to first draw its…

Q: а. 10х, + 2х, — х, 3D 27 — 3х1 — 5х, + 2х; — —61.5 X1 + x2 + 6хз — — 21.5

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Q: The domain of definition of Rx) = /log (log x) – log (4 – log x) – log 3 is (b) [10°, 10*] (d) (10°,…

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Q: The series E(-1)"-1. Vn+1 is conditionally n=1 convergent, but not absolutely convergent. Select…

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Q: 2. Find the Fourier series expansion of: | 0, f(x) = -1<x < 0 sin TX, 0 < x < 1 and then use it to…

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Q: 2. Find the arc length of the curve y= from x-2 to xD3 16 2x2

A: The solution is given as

Q: 2. 5, 15, 20.

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Q: 2- Use Eq. (1) to prove the recurrence relation: (n + 1) Pn+1 = x(2n + 1) Pn - n Pn-1

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Q: A firm estimates that it will sell N units of a product after spending x dollars on advertising,…

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Q: The matrix 29 -28 C = -56 1 56 24 -23 has two distinct eigenvalues such that 11 < 12. The smaller…

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Q: Use The Runge-Kutta Method SoNe the: dy X(I+x), y(0)=3,h20.2

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Q: 3. Graph the polar equation and find the area of the region. Between the loops of r = 2 – 6 cos 0

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Q: az Suppose z is a function of r and y, and csc Vr² + yz = 2"e»in z_ Solve for dz and dy

A: Given: csc x2+yz=zyesin x To find ∂z∂x and ∂z∂y.

Q: ĐUse the Fuler method's solve the: らゃう2び20 (o)1 れ:0r

A: We will use the formula of Euler method which is  yn+1 = yn + hf(xn , yn).  Then we will perform the…

Q: Q2: Find a root of x- 0.5 – 2-2x = 0 by using Newton-Raphson method correct %3D 4 decimals so that…

A: Given: f(x)=x-0.5-2-2x To find: Root of a given function by using Newton-Raphson method correct to 4…

Q: * dy/dx=(x+siny)/(2y-xcosy) is an exact equation false O true O

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Q: Find the eigenvalues 11 < 12 < 1z and corresponding eigenvectors of the matrix -3 4 -10 A = 1 The…

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Q: 25. The graph of y g(x) shown below is the transformation image of the graph of y = log,x. Kendra…

A: Given graph of function is