Find the number in the interval [0, 6] such that the number minus its square is as follows. (a) as large as possible (b) as small as possible

Q: For the equation given, evaluate dv 5exy - 4x = y 7 dy at the point (3, 0). (Round your answer to…

A: Given query is to find derivative at indicated point.

Q: Show

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Q: Let F(x) = f(x) and G(x) = (f(x))º. You also know that a³ = 2, f(a) = 2, f'(a) = 5, and f'(aº) = 9.…

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Q: 1 10+ e-5x -5x / 10 + 1 = = = 1 / (6-10 + 10) ) + 10 f - dx e e-5x 50 Evaluate s -dx. Hint: Multiply…

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Q: 4+x in two ways. 1. In this problem you will find the derivative of f(x) = X (a) Method 1: First…

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Q: When gas expands in a cylinder with radius r, the pressure P at any given time is a function of the…

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Q: 10) A lifeguard is watching a beach from a line of sight 6 feet above the water. She sees a swimmer…

A: ( 10 ) Given height above the water = 6 ft depression =8°

Q: Find lim sin x. .00

A: To evaluate the given limit of the function

Q: Find the local maxima, local minima, and saddle points, if any, for the function z = 2x² + 3y² - 16x…

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Q: The graph shows the position s= f(t) of a car t hours after 5:00 P.M. relative to its starting point…

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Q: Find the derivative of the function at Po in the direction of A f(x,y,z) = xy + yz + zx, Po(1,-1,2),…

A: Given f( x,y,z ) = xy + yz + zx P0 = ( 1 , -1 , 2 ) A = 2i + 6j -3k

Q: Use the table below to evaluate the derivatives below. T f(x) f'(x) g(x) g'(x) h(x) | h'(x) h(z)h(2)…

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Q: Use any method to find the volume generated by rotating the region bounded by the given curves about…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: nd dy for d²y dx² y(x) = cot(x)

A: Given query is to find indicated derivative.

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: y' = Differentiate y sin z 28

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Q: Evaluate the definite integral using Part 1 of the Fundamental Theorem of Calculus. 5 [36 sin (z)dz…

A: H=∫05π36sinxdxwe know  ∫sinxdx=-cosx

Q: 16x²64x25y² + 150y - 161 = 400 a) General Equation form b) Standard Equation form c) Distance…

A: As per our guidelines we can answer only 3 subparts of the given question, so kindly repost the…

Q: Find the linearization L(x,y) of the function at that point. f(x,y) = x3y4  (1,1)

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Q: Find the directional derivative of f(x, y) = exy in the direction u = (,) at (xo, yo): (0,1). 3545…

A: Given query is to find direction derivative.

Q: Find the integral using the substitutionu=t7. Enclose arguments of functions in parentheses. For…

A: Given query is to find the integral.

Q: Identify the rate of change (dy)/(dx) of y=x^(2)-2x when x=1

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Q: Sand falls from a conveyor belt at a rate of 14 m³/min onto the top of a conical pile. The height of…

A: rate=14 m3minhieght=38(base diameters)volume(V)=13πr2hwhere r is radius and h is height

Q: SHOW

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Q: Find the points where the tangent line to the curve y = 3x² - x³ is horizontal. Select one or more:…

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Q: Sand falls from a conveyor belt at a rate of 14 m/min onto the top of a conical pile. The height of…

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Q: If My - N₂ N equation = Q, where is a function of x only, then the differential M + Ny = 0 has an…

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Q: Find the equation of the tangent plane to the given surface at the specified point. z = y ln(x),…

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Q: Find f(x(t),y(t)) if ƒ (x,y) = x²y³, x(t) = 1 + t, y(t) = 1 − 2t. = — dt A. 2x³y³ + 3x²y² B. 2yx³ +…

A: Given data : Find f(x(t), y(t)) if f(x, y) = x²y³, x(t) = 1 +t, y(t) = 1 − 2t.

Q: Let f(x,y)=x² - xy + y²-y. Find the directions u and the values of Df(1,-1) for which the following…

A: As you have asked for multiple subparts so I will answer first three subparts as per the guidelines.

Q: Recently, a meme on social media was divvying up lottery winnings among everyone in the country.  If…

A: Recently, a meme on social media was divvying up lottery winnings among everyone in the country.  If…

Q: If the tangent line to the curve y = f(x) at (4, 3) passes through the point (0, 2), find f (4)

A: If the tangent line to the curve y=fx at 4, 3 passes  through the point 0, 2, then to find f4.

Q: 9 A person standing at a point some distance away from the base of an antenna tower measures the…

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Q: 2. Sax 3x arctan (2x) dx

A: Given integral:-  ∫3xarctan2xdx

Q: (a) When is the car speeding up? [8,16] (Simplify your answer. Type your answer in interval…

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Q: lim f(x) lim 8118 lim f(x) x → 1 lim_f(x) X-3 f(x) the equations of the asymptotes (Enter your…

A: We have given graph of the function  From given graph  limx→∞fx=-2 limx→-∞fx=2 limx→1fx = Does Not…

Q: Find the length of the curve. r(t) = cos(4t)i + sin(4t)j + 4 In(cos(t)) k, 0 ≤ t ≤ π/4

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Q: Find the highest point z and x, y of the paraboloid x² + y²². 10x+12y+z+8=0. 11

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Q: Vrite the given differential equation in the form L(y) = g(x), where L is a linear differential…

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Q: 2. Compute: S√2+e-3tj + (sin4t + 1)k] dt.

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Q: Suppose that the area, A, and the radius, r, of a circle are changing with respect to time and…

A: given  A=πr2given  drdt=2 cmswhen r=5 cm drndr=nrn-1

Q: Determine the point(s) on the surface z = 12x - 16y - 2x² - 4² at which the tangent plane is…

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Q: Find the limit. (I

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Q: f(x) = x + 6 x² +6 2

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Q: A heavy-duty shock absorber is compressed 4 cm from its equilibrium position by a mass of 700 kg.…

A: According to question,Given data,Mass = 700 kg,g = 9.8 ms2,A heavy duty shock absorber is compressed…

Q: Evaluate the integral -4 √ (z+a) (x + b) dz dx for the cases where a = b and where a ‡ b. Note: For…

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Q: Find the radius of curvature of the following curve at the given point. Then write the equation of…

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Q: Write an equation for the function graphed below -7 -6 -5 -4 -3 y = 5 4+ 3- 2 1 -2 -3 4 5

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Assume that all variables are implicit functions of time t. Find the indicated rate. dy dt dy x² +…

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Q: Suppose that a certain population obeys the logistic equation dy = ry(1-2). dt a) If yo= find the…

A: Given that , dydt=ry1-yK