Find the general solution of the given higher-order differential equation. y"" + 3y" + 3y' + y = 0 y(x) =

Q: If f(x) < g(x) for all x # c then limit of f(x) at c is less than the limit of g(x) at c.

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Q: QI @ Find fx and fy for the following function: (i) f(x,y)=(x²-1)(y + 2) (ii) f(x,y)= ex+y+1 (iii)…

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Q: A ship sails South 2 km, then turns West. If it sails at a rate of 10 kph, find the rate at which it…

A: A ship sails south 2km, then turns West. Rate of ship sailing = 10kph

Q: ind the marginal cost, marginal revenue, and marginal profit functions. C(x) = 7x; R(x) = 9x −…

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Q: 8 7 b S f(x)dx – f f(x)dx = ƒ ƒ(x)dx 5 5 a

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Q: Because the derivative of a function represents both the slope of the tangent to the curve and the…

A: The solution is shown in step-2

Q: 3. Use the limit definition to calculate the slope of the tangent to the curve f(x) = x² + 3x-5 at…

A: The given curve is

Q: Suppose ∞ 522 f(x) = Σn! (x - 7)" n=0 To determine [ƒ(a) da to within 0.0001, it will be necessary…

A: To find

Q: Find the area of the region bounded by the curves y=2² and y= 2²+

A: Given :- The region bounded by the curves  and To Find :- The area of the region

Q: Find a polynomial function of least degree having only real coefficients, a leading coefficient of…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: If f(x) = g(x) for x # c and f(c) # g(c) then either f or g is not continuous at c.

A: Continuous Function:In mathematics, a continuous function means that a continuous change in the…

Q: Use the derivative f' to determine the local minima and maxima of f and the intervals of increase…

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Q: Consider the equation 5x²+16x = 625X-8 Enter the number of solutions of the above equation.…

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Q: sin 8-1 Ө lim- 8-00

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Q: Answer the questions and provide examples as instructed: 1. What do you think that lim f(x, y, z)= L…

A: Given the limits of function.

Q: Consider the following. x=t², y=In(t) (a) Eliminate the parameter to find a Cartesian equation of…

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Q: SET D4 Differential Equations Note: If you have already answered the problems in this post, kindly…

A: The given differential equation is  .Consider  where  .The differential equation becomes  .  Its…

Q: Find (without using a calculator) the absolute extreme values of the function on the given interval.…

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Q: Find the vector x determined by the given coordinate vector [x] and the given basis B. B= 1 6 - 6 4…

A: The solution is shown in step-2

Q: A piece of cardboard measuring 14 inches by 9 inches is formed into an open-top box by cutting…

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Q: Find the area of the shaded region. -4 x = y² -3 -2 y 2 -2 -3 y = 1 X = e) 2 y = -1

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Q: Suppose that f(x) is a function with f(85) = 43 and f'(85) = 6. Estimate f(86).

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Q: Explain why 4-4 using the relationship between radical expressions, rational exponents, and…

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Q: Determine the instantaneous rate of change f(x)= x^2-3x at x=-2.

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Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

A: Graph

Q: 9.) Find a set of parametric equations for the tangent line to the curve of intersection of the…

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Q: Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as…

A: To find all complex zeros of the following polynomial function.

Q: specified step size to estimate the value of the solution at the given point x* Find the value of…

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Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

A: The indicated function  is a solution of the given differential equation.By using the reduction of…

Q: Find all values x = a where the function is discontinuous. 6. f(x) = -3/(6x - 8)(8 - 2x)

A: A function is said to be discontinuous at a point where it is not defined.

Q: Let R(x) = √² Find the limit below. Show all steps and justify each step. R(x) x² lim x18 √1+t²dt.

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Q: The current in an electrical circuit is given by the formula I = the time, in seconds. t+2 15-t'…

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Q: Determine the intervals on which the following function is concave up or concave down. Identify any…

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Q: cos 2x + C₂ sin 2x = 0 = 0 = 0 + 4y = 0 = 0

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Q: Q4 Find the following integral. Show all your work. (2 si 2 sin (20) - 3eº 0³ +1 O√O +π. In (0))) 0…

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Q: Determine the global extreme values of the function ƒ (x, y) = x³ + x²y +9y² on x, y ≥ 0, x + y ≤ 4.…

A: The solution is shown in step-2

Q: Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies.…

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Q: Sandra is a 25-year-old woman who weighs 120 lb. She burns 300 - 50t cal/hr while walking on her…

A: Given calories burn (300-50t) calories per hr.Calories intake 80t in t hr.

Q: ρπχ-1 x-0 tan (2x) b) lim

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Q: Express f(x) in the form f(x)=(x-k)q (x) + r for the given value of k. f(x)=x³ +5x² + 9x+6, k = - 2

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Q: Find the following limits, if they exist. If they do not, state whether they are infinite limits or…

A: We have to find the limits of

Q: If t= 140 1 + 3e-0.25t || = 70, solve for t.

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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: Let f(x) = 8x sin ¹(x). Find f'(x). f'(x) = Find f'(0.4). f' (0.4) =

A: Let To find .To find .

Q: Solve the problem. Round your answer, if appropriate. 20. A ladder is slipping down a vertical wall.…

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Q: Determine the interest rater needed for an investment of $4,000 to grow to $8,000 in 3 years if…

A: If an initial investment of value P(in dollar) is compound Continuously at the rate r for t  years,…

Q: (a) Find the linearization of the function f(2)=√√ at a = 4. b) Use your answer in (a) to…

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Q: Find the area of the surface cut from the paraboloid x² + y² - z=0 by the plane z = 2. The surface…

A: The given paraboloid is

Q: 4. A 15-foot long ladder rests along a vertical wall. Its top slides down the wall while its bottom…

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