Find the solution of the given initial value problem in explicit 1 y' = (1 — 11x)y², y(0) = ——— 6 y(x) =

Q: Verify the product law for differentiation, (AB)' = A'B + AB' where A(t) = To calculate (AB)', first…

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Q: Distance Between Two Ships Two ships leave the same port at noon. Ship A sails north at 12 mph, and…

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Q: Q3/ Answer one from the following :- 1- Determine the general solution y(x) for the equation 2y" -…

A: Explanation of the answer is as follows

Q: 1. Determine whether the series n=1 3n+1 ln(n+1) is convergent or divergent.

A: : since,1< ln(n+1),for n>2 so, 0<(n^2)/(((3^(n+1))*ln(n+1))<n^2/n^4=1/n^2,  since…

Q: 26 Functions f(a) and g(x) and their first and second derivatives evaluated at z = 1 are listed as…

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Q: Distance Between Two Cars A car leaves an intersection traveling east. Its position t sec later is…

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Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: Concept: Wronskian method: W(x1(t), x2(t), . . . , xn(t)) =x1(t) x2(t) · · · xn(t) xx1'(t) x2'(t) ·…

Q: State the order of the given ordinary differential equation. (sin e)y"" - (cos e)y' = 3 Determine…

A: The order of a differential equation is the order of the highest derivative present in the given…

Q: 12-1 40-8 Let A = -4 and b = b₂ Show that the equation Ax=b does not have a solution for all…

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Q: 5 Determine the interval of convergence of the series (e-4)" and within this interval determine the…

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Q: ¹.) f(x) = (x³ - 7x² - 6x + (4 +17) f(x) = x-6 7x - 6 2) f(x) 4 - 17x²

A: Explanation of the answer is as follows

Q: Given the equation z = arctan(x- y²) with the change of variables x=s³-t³ and y=st² + s²t, use the…

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Q: 10 Let u= (1, 2, -1) and v= (3,-1,2) be two vectors in Rª. Which of the following is a normal vector…

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Q: 11. Use L'Hopital's rule to find the following limits. x² + 3x-4 x-1 (a) lim x-1 In x xx-1 (b) lim

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Q: 1) a car is slowing down at the rate 0.8 ft /sec², How the will the can move before it stops if its…

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Q: Find the solution to the differential equation below such that y(0) = 14 y' = 10xy - 2x y(x) =

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

Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

A: This question can be solved using the concept of Laplace transformation.

Q: Let y = f(x), where f(x) = 5x² + 5. Find the differential of the function. dy = X

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Q: 2- Find xyz dV where D is the region with -1 ≤ x ≤1, x ≤ y ≤ 1, above z = x, and below z = y + 2. D

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Q: 3t 2t - 1 1-t 1+t [][] 3 and B(t) = 51² 51³ t Verify the product law for differentiation, (AB)' =…

A: See the details solution in below

Q: Identify and sketch the graph of y = r²+1 in R³.

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Q: Given a function, Based on the function, S-3 F(s) = 2 S² +6s+13 a) Determine ƒ(t). b) Based on…

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Q: 4.2.2. Find the integrating factor by inspection then solve the following differential equation.…

A: A detailed solution is given below.

Q: 5(c) Find the rectangle with the largest area that can be inscribed in the top half of the ellipse ²…

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Q: A farmer has 400 yards of fencing and wishes to fence three sides of a rectangular field (the fourth…

A: A farmer has 400 yards of fencing and wishes to fence three sides of a rectangular field.

Q: If lim f(x) = ·∞ then which of the following is true?

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Q: Solve the equation | +6 - 4. The solutions are 1 = and 2 = where ₁ ≤ x2. This means x₁ is the…

A: Given,  |x+6|=4

Q: Find the solution to the differential equation below such that y(0) = 14 y' = 10xy - 2x y(x) =

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 3) Suppose f (x, y) is a differentiable function. a) If (a, b) is a critical point of f (y) (in the…

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one.

Q: Given the function z= f(x, y) = ln(x² + xy - y²), find the following: a) Find gradient at the point…

A: As per our guidelines we are supposed to answer only first three subparts of the question. Kindly…

Q: Given the function z = f(x, y)=x²y+2y² + 4xy-2, find the following: ) Find all of its critical…

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Q: 12 Let A be a square non-invertible matrix. Which of the following is not true? Select one…

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Q: Evaluate: limt o sin 3t t5 (t-1)² using L'Hôpital's

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Sx² 1 if if > 2 x f(x) = 5 3 if x < 2 af is differentiable at x = = 2 bf is continuous at x = 2 cf…

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Q: The graph of f is given below. -2.5 -2 -1.5 Why is f not differentiable at = -1? Of has no tangent…

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Q: The derivative of sec22x(cos2x−sin2x) with respect to x is?

A: I have appended the formula used in the solution part of the question

Q: Find y' tan³ (5x - y) + cos ¹(5x - y) = 100

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Q: Find the general solution of the given differential equation, and use it to determine how solutions…

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Q: 0 Given the piecewise function f(x) = 5-x 5-z What is f (4) ? Answer: f4 (4) = What is f¹ (4) ?…

A: Given function:-

Q: 7. Determine the dimensions of a rectangular box, open at the top, having a volume of 32 ft³, and…

A: Given :Volume = 32 ft3

Q: Which one of the following is the domain D for f(x, y) = ln (2²-(y-2)²) ? Select one alternative:…

A: The given function: fx,y=lnx2-y-22.We need to find the domain.

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

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Q: In a certain region there is a uniform current density of 15.0 A/m2 in the positive z-direction.…

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Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 9 27…

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Q: • Find the volume generated by revolving area about the given line plane the given

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Q: Give the general equation of the plane containing the point (3,-1,4) and perpendicular to the line =…

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Q: 10. S sinh rai tanhxainhr-tenha -dx

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Q: How. Find the lengths for the following curver. 7 \- r = 1 + cosa

A: I am attaching image so that you understand each and every step.

Q: Given f(x, y, z) = ze™" - a sin none of the choices 02-1/ 02²/ 0 01- ¹(), what is fax (0,2,1)?

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Q: Find a particular solution of the indicated linear system that satisfies the initial conditions x₁…

A: Please see the below picture for detailed solution.