Evaluate the limit using L'Hôpital's Rule. 8 0-2 HIL lim x 0 4(e- e *) sin(2x)

Q: Given an acceleration vector, initial velocity (uo,vo), and initial position (xo.Yo), find the…

A: Here we have to find the velocity vector.

Q: Find the area of the region bounded by one petal of the curve given in polar form by the equation r…

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Q: You are standing above the point (4, 3) on the surface z = 30- (3x² + y²). (a) In which direction…

A: Given point is (4,3) on the surface z=30-(3x2+y2)

Q: A street light is at the top of a 18 ft pole. A 5 ft tall girl walks along a straight path away from…

A: As given the girl walking away from pole with a speed of 7ft/sec.Height of the pole is 18ft and girl…

Q: AB2: Let G(x) = ef(x). Find G'(6). AB3: Evaluate xf'(4-x²) dx S²x₁

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Q: Express the given quantity as a single logarithm. =1/12 In((x + 2)9) + [in(x) - In((x² + 3x + 2)²)]…

A: f(x)=19ln(x+2)2+12lnx-ln(x2+3x+2)2we know lnxn=nlnxlnab=lna-lnb

Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

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Q: Find a plane containing the point (-2,-1,3) and the line of intersection of the planes -5x + 5y-7z =…

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Q: Let f(x) be a function that is differentiable on the entire real line. If f(-5) = 0 and f(1) = -8,…

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Q: ON 11 Solve the initial value problem. dr Differential Equation: dt Initial Condition: r(0) = -4i +…

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Q: Find the following for the function f(x) = 3x² + 4x -2. (b) f(1) (a) f(0) (e) - f(x) (f) f(x+3) (a)…

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Q: shift of the graph as described in the lesson, what values of m and n will make the graph of…

A: We will find the required.

Q: Consider the following function. h(t) = + = 6 Find the derivative of the function. h'(t) = X Find…

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Q: The sales of a plastic widget were estimated to be: P(t)  =  6000 t e−0.1t where t is in weeks,…

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Q: Let 7 sin x + 7 cos y = 5. dy dx d'y dx² 5 cos x 7 sin y 0

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: The pressure, volume, and temperature of a mole of an ideal gas are related by the equation PV =…

A: The pressure, volume, and temperature of a mole of an ideal gas are related by the  equation…

Q: lim f(x) = L and lim f(x) = M, where L and M are finite real numbers, then how are L and M related…

A: Given query is to find relationship between L and M.

Q: Suppose you have a cache of radium, which has a half-life of approximately 1590 years. How long…

A: Given: Half-life of radium = 1590 years To find: Time taken to disappear 1/6 of the radium. Formula…

Q: Consider the following position function. Find (a) the velocity and the speed of the object and (b)…

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Q: Use the first derivative and the second derivative test to determine where each function is…

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Q: An object is dropped from a tower, 144 ft above the ground. The object's height above the ground t…

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Q: A fox population in a certain region is decreasing at a rate of 4% per year starting with an initial…

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Q: A water tank in the shape of a hemispherical bowl of radius 5 m is filled with water to a depth of 2…

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Q: 1) y(x) = x, y₂(x) = z lnx, and y(x) = z² are solutions to a third order differential equation.…

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Q: Find the absolute maximum and minimum of f(x, y) = 2x + 4y within the domain x² + y² ≤ 25. Please…

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Q: A function f is defined for all x. Use the raph of f' to decide: a) Over what intervals is f…

A: Here we have to observe the graph.

Q: 1 At what value of x, f(x) = x(1-x) attains its absolute minimum value over the interval [2,3]?

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Q: f(x)=x²-2x+5 X= (Simplify your answer, including any radicals as needed. Use integers or fractions…

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Q: Consider the function f (x, y) = 5x² - 6y². Find the directional derivative of f at the point…

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Q: The graph of y = f(x) (solid) and its tangent line at (-3,-4) (dashed) is shown. 10 9 8 7 6 5…

A: Given graph of a function f(x) and it's tangent at x=-3

Q: Solve equation (10) from Section 7.4 + ["i(t) dr = E(t) (10) L+Ri(t) + dt subject to i(0) = 0 with…

A: The given differential equation is: Ldidt+Ri(t)+1C∫0t i(τ) dτ=E(t)

Q: Suppose that f(x, y) = y√ x³ + 1 on the domain D = {(x, y) | 0 ≤ y ≤ x ≤ 2}. Then the double…

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Q: f(x,y)=√y-5x-8 Find the domain of the function. Express the domain so that coefficients have no…

A: The given function fx, y=y-5x-8. We have to find the domain of the function and sketch its graph.

Q: North West Northwest Southeast Possible answers 125° 90° No Answers Chosen No Answers Chosen No…

A: We have to sort the given angles based on general direction. Since we have the direction chart…

Q: -6 -5 -4 -3 -2 -1 Find the following limits. f(x) lim 2-17 g(x) = 6+ 5 3 2 -1 -2 -3- ينا -4 -5 -6+ "…

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Q: line to the graph of y = g(x) at x = 4 is 4x+12y = -56 It follows that y = is the equation of the…

A: Given that at x=4, 4x+12y=-56 is a tangent.

Q: Find the volume of the solid obtained by rotating the region bounded by the curves: y = x²/9, x =…

A: To find the volume of the solid obtained by rotating the region bounded  by the curves. y=x29,…

Q: Given the function f and point a below, complete parts (a)-(c). f(x) = 2x², x ≥ 0, a = 4 a. Find…

A: Use the basic concept of derivative and put the given value then simplify.

Q: 01) Let v(t) = 36-6t - 6t² be the velocity function of an object in rectilinear motion for t≥ 0.…

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Q: Find all critical points and then use the first-derivative test to determine local maxima and…

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Q: How many of the following equalities are correct?…

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Q: Find a function f(x) such that f'(x) = 7e² + 4x and f(0) = −2 f(x) =

A: We need to find out the function.

Q: 2 W S 395 X Find the distance from the point (-9,7,4) to the line ä(t) = (-3, 2, 4)t + (2, -3, 8).…

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Q: The graph of y = f(x) (solid) and y = g(x) (dashed) is shown -6 -5 4 -3 f(x) lim 2-1 9(2) -∞ 00 8…

A: The given graph is:

Q: Find the radius of convergence R of the series. n Σ ; (x - a)", b > 0 1- σπ n = 1 R = Find the…

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Q: Use linear approximation, i.e. the tangent line, to approximate 8.2 as follows: Let f(x) = x. The…

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Q: Find all the value(s) of x for which each of the following matrices is non-singular (i.e.…

A: According to bartleby guidelines we supposed to do the first one of multiple questions  kindly…

Q: QUESTION 18 Given that the x- and y-coordinates of a moving particle are given by the indicated…

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Q: I'm confused on how you got 1.905 in the numerator

A: Pi = 3.14    The rate of volume of gravel dumped is: dv/dt = 10 In circular cone relation between…

Q: 5 [²₁x² - 4x +31 dx

A: The given integral ∫05x2-4x+3dx. We have to find the integral.