Find the directional derivative of the function f = In (x² + y2) at the point P(4,5) in the direction of the vector a = î -Ĵ

Q: Consider the non-linear system i = x² – 4. - 7) How many equilibrium points does the system have? 8)…

A: Given that x'=x^2-4 So the equilibrium solution are x=2 and x=-2

Q: Find the equations of the normal line to the surface z = 3x'y at the point (-2, -2, -1536) ++-1536…

A: We have to find the equation of normal lines to surface at the point

Q: 17. If 2 D. x -2 2x 18. Given that 2/3 19. The range of values ofx for which -1 B. -5 -5 D. x…

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Q: Ans. X = 3, C. V. = 40.67 % %3D %3D Q.48 The first four moments of a set of numbers about 3 are 2,…

A: Let's denote the moment about 3 by M. So it is given that M1=-2, M2=10, M3=-25 and M4=50. The…

Q: Q.10 Let A denotes a card of heart, B a faced card. A and B are their complementary events. If a…

A: Let A denotes a card of heart and B denotes a face card. Thus, we have, P(A) = 13/52 P(B) = 12/52 We…

Q: A uniform magnetic field B has constant strength b teslas in the z-direction [1.e., B = (0, 0, b) 1…

A: Stoke's theorem ∫CF→.dr→=∫∫S curlF→.dS→ Where S is a smooth surface bounded by a smooth closed curve…

Q: If f(3) = 8, f'(3) = 0 and f'"(3)= – 4, then O 3 is a local minimum value for f(x). O 3 is a local…

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Q: Q.13 Two dice are thrown once. The following events are defined: A = sum of spots is 6 B = sum of…

A: Note: Hi there! Thank you for posting the question. As there are multiple sub parts, according to…

Q: Q1/ Use Lagrange multipliers to find any maximum or minimum volumes: i) z = f(x,y) = 5 – 3x – 4y and…

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Q: Change the experiment of Problem 8 so that the constant harvesting doesn't start until time t = 5.…

A: To find the general solution for the modified differential equation in problem 12, where constant…

Q: 6) The largest controllable eigenvalue is

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Q: Problem P3. In a factory, machine A manufactures 20 % of the bolts; machine B manufactures 30 % of…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

Q: 7-10 Evaluate the double integral. y -dA, D={(x, y) | 0 <x< 4,0 < y < Vx} 7. x² + 1 9. dA, D= {(x,…

A: WE HAVE SOLVED THIS PROBLEMS BY THE RULES AND FORMULAS OF INTEGRATION.

Q: Let S be a closed n-cube with v(S) > 0. Suppose g, h : S → R are two bounded #3 and integrable…

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Q: Suppose that f(x, y) = x³y². The directional derivative of f(x, y) in the directional (1,-2) and at…

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Q: 2. Which of the following binomials is a factor of the quadratic expression, three x-twenty-six x +…

A: Consider the quadratic expression: 3x2-26x+16

Q: Find the area of the region between y = sinx + 5 and y = 0.6 for 5 ≤ x ≤ 11. Round your answer to…

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Q: 8. dr+ (2r cot 0 + sin 20) d0 = 0.

A: This will be a linear differential equation of r. We will write this in standard form and then solve…

Q: Suppose f: R → R is defined by the property that f(x) = x + x² + x³ for every real number x, and g:…

A: The given function is f(x)=x+x2+x3, and g∘fx=x for all x. Statement: f∘gx=x for all x. We have to…

Q: A box contains 3 Black, 4 Red, 5 Blue. Then the probability of drawing 3 balls randomly with same…

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Q: Find a possible formula for the graph. f(x) = 2 Y 5 10 X

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Q: Find a possible formula for the graph. a 7-6-5-4-3-2-1 123 567 O g(x) = O g(x) = -k(x + 1)(x -…

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Q: Solve for M -76-2(m18)-9

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Q: Solve  5+8

A: Given sum, 5+8

Q: Using the coordinates for points A, B, and C provided in Table 1 and plotted in Figure 1, answer the…

A: We shall only answer first Que as asked in next step.

Q: Convert the point or decimals to at least one decimal place, with positive val (+0,2)=

A: To convert the point (-5, 5, -3) to cylindrical coordinates, we need to determine the values of the…

Q: -[: :]. »- [:]. - Let A B = and X = Solve the following linear system of equations: AX=B. Let A, B…

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Q: Use the factorization A=QR to find the least-squares solution of Ax = b. 1 22 A= b= -22 23 23 -22 1…

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Q: Let f(x) = x². Find the upper and lower sum for the region bounded by f(x), the x-axis, x = 0 and x…

A: Given,fx=x2Lower Limit, a = 0Upper Limit, b=3Number of rectangles, n=6

Q: Problem #5: Consider the system of linear equations given in problem 4. Calculate: a) L and U…

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Q: c) s² L(y(x)) -sy(0)-y'(0) Q12) The kernel of the Laplace transform of f(t),t> 0, is: d) s²…

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Q: Compute the least-squares error associated with the least-squares solution x of Ax = b. A = 1 - 1 0…

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Q: Problem P4. If P(A) — 0.22, Р(B) — 0.25, Р(С) — 0.28, P(AN B) 3D 0.11, Р(ANC) 3D 0.05, P(BПC) %3…

A: Hey there! As per our policy we can answer only 3 sub-parts at a time. Please make a new request for…

Q: 2. State and prove the Cantor's Intersection Theorem.

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