If u =< sin 0, - cos > and Vƒ (−2, 5) = 3u, then the minimum value of the directional derivative Du f(−2, 5) is attained in the direction of u.

Q: Question 2: Tutorial 10 x² and g(x) (b) If f(x) x³ with x € [1,1], find the c € (-1, 1) by using…

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Q: (8) A LTI system is described by the D.E. y +6 Y+8y -2t find h(t) then find y(t) if X(t) = te²t tro-

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Q: Question 13 Write a system of equations to model the problem. Be sure to define your vairables.…

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Q: The integral of the right hand member of the first order LDE A B C с D -2sin³0 3 COS 2 2sin³0 3 sin…

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Q: (b) Find the critical points. (c) For each critical point, find the corresponding linear system.…

A: Given system is dxdt=x(-1+2.5x-0.3y-x2)dydt=y(-1.5+x) Let f(x,y)=x(-1+2.5x-0.3y-x2)g(x,y)=y(-1.5+x)…

Q: Use the transforms of some basic functions (i.e., theorem 4.1.1 in the textbook) to find ¹£{f(t)}•…

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Q: 2. State why the function f(z) = 2z²-3-ze²+e-² is entire.

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Q: Use the inverse transforms of some basic functions to find the given inverse transform. x-1,² 9s…

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Q: 3.2 Example. Consider the Dirichlet function f: [0, 1] → R defined by if x is rational f(x)= if x is…

A: To Prove: Dirichlet's function which is defined as f:[0,1]→ℝ, f(x)=1x∈ℚ0x∈ℚc  is not Riemann…

Q: i) ii) (P V Q) ^ -(P AQ) (P Λ Ο ^ R) V (P ^ →Q ^ R) V (Ρ ^ ¬Q ^ ¬R)

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Q: 3 A ITI system is described by the D.E. Y +6 Y+8y=2XL) -2t find h(t) then find y(t) if X(t) = te²t…

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Q: Suppose a unit of capital costs $2 and a unit of labour costs $4. The production function is Q = 6KL…

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Q: Question 13 Write a system of equations to model the problem. Be sure to define your vairables.…

A: Introduction: A finite collection of equations for which we searched for common solutions is…

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A: Let f(x)=xn-an. Now using binomial expansion…

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Q: . (a) How many quadratic residues are in the residue set Z19? (b) Determine if 4 and 9 are quadratic…

A: (a) Let p be an odd prime. There are p-12 quadratic residues  in ℤp Hence there are total 19-12=9…

Q: Embassy Motorcycles (EM) manufactures two lightweight motorcycles designed for easy handling and…

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Q: Write the given system in the matrix form x' = Ax+f. r(t)=9r(t) + cost e(t)=r(t)-20(t)-4 Express the…

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Q: Find the equation of the line joining the points (4, 1) and (1, 9)

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Q: Which of the following subsets of P2 are subspaces of P2? □Ā. {p(t) | √√√p(t)dt = 0} B. {p(t) | p'…

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Q: dy__=1 with the homogenous substitution method. Solve explicitly. 7. Solve the equation dx x² X…

A: Introduction: If the degree of both f(x,y) and g(x,y) is the same, a differential equation of the…

Q: Reduce each of these quantities to a real number: (a) 1 + 2i + 3 - 4i 2-i 5i (b) 5i (1 - i)(2 - i)…

A: (a) Here given the complex number 1+2i3-4i+2-i5i to reduce this complex number first take the HCF of…

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Q: 4.8. Show that Dirichlet's function 1, if x is a rational number, { otherwise f(x) = 0, is not of a…

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Q: 2. 2-3i, assuming x > 0 3. e3r-5ri 4. x5+2i, assuming x > 0 I

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Q: You can afford a $1400 per month mortgage payment. You've found a 30 year loan at 8% interest. a)…

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Q: Write Mindanao is not part of the philippines in logical form then write the truth value

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Q: 6. 3π -<x<27. Draw the angle in the coordinate 2 plane in the appropriate quadrant IN THE SPACE…

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Q: DISCRETE MATHS (GRAPH THEORY) Based on the images attached, determine whether the following graphs…

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Q: Find the radius of convergence, R, of the series. (x - 10)" n R = 10 ∞ n = 1 I = Find the interval,…

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Q: Question 13 Write a system of equations to model the problem. Be sure to define your vairables.…

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Q: Write an equation for the transformed logarithm shown below, that passe through (3,0) and (0,3) 3…

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Q: 9) Find and perform each of the following for the given functions. a. All zeros and their respective…

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Q: . (a) How many quadratic residues are in the residue set Z₁9? (b) Determine if 4 and 9 are quadratic…

A: Introduction: Quadratic residue is a part of congruent modulo theory. It is a non-linear congruence.…

Q: t) = y"+y= √2sin(√√√2t), y(0)=9, y'(0) = 0

A: Given,        y''+y=2sin2t, y(0)=9, y'(0)=0

Q: [1 0 1/3 0 1 1/3 0 0 1/3 Numerically verify that each initial state vector xo has the given…

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Q: Consider the function f(x) = 2 - 7x² on the interval [ - 5, 7]. Find the average or mean slope of…

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Q: Show that the function y1 = 1 / t is a solution of the first order Riccati differential equation…

A: Given differential equation is y'=1t2-1y2- 1t2-1 Rewrite it,  y'=1t2-1y2-1  ------(1) Also, given…

Q: 5. Let y(t) be the solution of intial-value problem y"- 2y + 10y=f(t), y(0), y(0)-8 where f(t) =…

A: Here first we convert the function into Heaviside function and then use the table of Laplace…

Q: = Consider the function f(x) 2 - 2x² on the interval [2, 3]. Find the average or mean slope of the…

A: We have to find the average slope of the given function using the formula f-3-f-23--2. For this, we…

Q: 2) Given the following: f(x)=x²+2x+1; g(x)=x-1; and d(x) = √√x + 3, evaluate a. f(h+2) b. d(g(7)) C.…

A: a. f(h+2)= (h+2)^2+2(h+2)+1 = h^2+4+4h+2h+4+1 = h^2+6h+9 b. g(7)= 7-1=6 d(g(7))=9^(1/2) =3

Q: Describe the steps in words that you would use to show that (x - a) is a factor of xn - an. Your…

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Q: The given vector functions are solutions to the system x'(t) = Ax(1) [1-4] x₁ = e Determine whether…

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