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Q: Use Definition 7.1.1. Definition 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

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Q: Find a unit vector u in the direction opposite of v = (2,8,-3).

A: Solution ) v =  { 2 , 8 , -3 }   vector with same magnitude and opposite direction   = { -2 , -8 , 3…

Q: The triangle with side length a=6 cm and angles measures angle B= 45° and angle C= 120° is given.…

A: Given data:- Side length of the triangle, a=6 cm ∠B=45°∠C=120°

Q: Talse. If f is not piecewise continuous on [0, co>), then {f(t)} will not exist. True False

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Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

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

Q: Which equation of a circle has the center, C, and radius, r, as shown in the graph? -3-2 7 T of 7 T…

A: The circle has center C3,-2 and radius 26

Q: Use the Laplace transform to solve the given initial-value problem. y(t) = y""+ 2y" - y' - 2y =…

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Q: Find the Taylor series generated by f at x=a. f(x) = 5x , a = 7

A: We have to find Taylor series of f(x) =5x about x=7. Let us see first what is Taylor series…

Q: Find the infinite sum of the geometric sequence with a = 4, r = Soo = > Next Question if it exists.

A: Topic-geometric Progression

Q: Which is the focus and directrix of the parabola with equation (y + 0.5)² = 4(x - 1)? Focus…

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Q: (a) Consider the boundary value problem (BVP) y" - 49y=tan(7x), y(0) = 0, y(n/7) = 1. Does this BVP…

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Q: Find the total area of the shaded region. 1.5- 1- 0.5- 0 y x=12y³ 6 x=12y² (12,1) 12 18

A: The equation of the curves are: x = 12y3 x = 12y2 The graph of the curves is To evaluate: The area…

Q: 3. Find the Taylor polynomial of degree 3 centered at x = 4 for the function defined by f(x)=√x.…

A: To find out the Taylor polynomial of degree 3 for the given function and also find out the value of…

Q: 5. Find the center of mass of a thin wire in the shape of the semicircle x² + y² = a², y ≥ 0, with…

A: Concept: The formula for the mass: m=∫Cρ(x,y)ds The center of the mass (x,y) is given by:…

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: a) b) z c) 5√5 d) none 5√5 18. Find the ranges of values of x for which the curve y = x4 - 6x³ +…

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Q: Identify this surface, φ = π/3 in spherical coordinates, and find its equation in x, y, z…

A: Identify this surface, φ = π/3 in spherical coordinates, and find its equation in x, y, z…

Q: Determine whether the differential equation is exact. If it is exact, find the solution. (7x² − 2xy…

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Q: 1. Find the maximum value of f(x, y, z) = x + y − z subject to the constraint x² + y² + z² = 6.

A: f(x,y,z)=x+y-z   x2+y2+z2=6 Rewrite it as: x2+y2+z2-6=0 L(x,y,z,λ)=(x+y−z)+λ(x2+y2+z2−6) Find all…

Q: D) lim f(x)=| 23 E) lim → 8 f(x) = F) lim f(x)= z 2

A: D) we know that, limx→3f(x)=limx→3+f(x)=limx→3-f(x)But limx→3+f(x)=2limx→3-f(x)=-1Since…

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: Let's find inverse Laplace transform.

Q: 3. Let o(a) be a solution to the initial value problem: y" + 2y' + 5y = 0; y(0) = 0, y'(0) = 4.…

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Q: Use linear approximation, i.e. the tangent line, to approximate 27.1 as follows: Let f(x)=x. The…

A: Our Aim is to find the approximation for 27.13 using linear approximationgiven that f(x)=x3.

Q: Answer true or false. If L{f(t)} = F(s) and L{g(t)} = G(s), then £¹{F(s)G(s)} = f(t)g(t). True False

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Q: Find the value of (2) for a solution (x) to the initial value problem: y" + 4y + 4y = 2x + 6; y(0) =…

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Q: enshot (1603) Solve the given differential equation. All solutions should be found. (3y² + 2xy) dx −…

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Q: Question Given f(x) below, find f'(x). Provide your answer below: f'(x) = f(x) = fot t¹ dt

A: The given data is: fx=∫xx3t4dt  To find the value of f'x

Q: 3x + 7 Consider the function f(x) = 4x + 1 and (A, ∞o) where the function is not defined at A. Find…

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Q: Use Green's Theorem to evaluate the line integral along the positively oriented curve C that is the…

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Q: An automobile company is ready to introduce a new line of cars through a national sales campaign.…

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Q: Tab Window Help ving Exponer X + -integrals-involving-exponential-and-log wolving Exponential and…

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Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 15 inches above the…

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Q: -9-8-7 6 5 4 3 C Ce N f 5 w N www T P Mar www ww S d Write an equation for the ellipse graphed in…

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Q: Determine whether following series convergent or divergent. Indicate the test you are using. If you…

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Q: Use the Laplace transform to solve the given initial-value problem. y(t) = 2y"" + 3y" - 3y - 2y =…

A: The given differential equation is; 2y'''+3y''-3y'-2y=e-t,y(0)=0,y'(0)=0,y''(0)=1.

Q: The circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm. Use linear…

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Q: Determine the points of discontinuity for the following. 2x+5 f(x) = X-7x+6

A: F(x)= (2x+5)/(x^2-7x+6) Factorise the denominator F(x) = (2x+5)/(x-1)(x-6) Denominator can not be…

Q: 21. If u = - y+z a) 0 Z z+x x+y b) 1 ди then the value of x + y + z 2 is: c) u d) None 22. The…

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Q: Q4) A- Graph the following functions and determine (domain, range): (1) y=sin/x/ (2) y=/x²-2/ (1) y…

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Q: Which of the following is the vector projection of (1, 0, 1) onto (-2,4,0)? 1 B. (-1,2,0) C.…

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Q: JS FdS, where F(x, y, z) = xi+yj + zk and S is the part of the cylinder S x²+y² = a² (a > 0) lying…

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Q: Evaluate the line integral curve C′ : x = 4 cost, y = 8 sint (0 ≤t≤7) NOTE: Enter the exact answer.…

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Q: PART 2: Obtain the general solution dv V dP P Obtain the particular solution y' = 1 + y² such that…

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Q: Consider the following function and point. x + 4 (5,9) X-4 (a) Find the derivative of the function.…

A: The given function is fx=x+4x-4, 5,9

Q: Find the equation for the slope of the tangent line to the curve below at any point (x,y). 2x + 5y =…

A: Given, 2x+5y=3y

Q: Equations of the form r=a sin (m0) or r= a cos (m0), where a is a real number and m is a positive…

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Q: 1 3 The x value(s) of the points where the tangent lines to the curve ³-4x that have a slope equal…

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Q: Find the radius of curvature of the curve y = √√x at x = 1 5√5 2 5√5 b) Sys c) 5√5 d) none 2 a) ind…

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Q: Let f be a function defined for t 2 0. Then the integral {f(t)} =[e-stf(t) dt is said to be the…

A: We need to find Laplace.

Q: Find f"(x) if f (x)=√√5 - 4x. Show work:

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