Solve the equation on the interval [0, 2π). 4 sin2? = 1 − 4 cos(2?)

Q: 3. F (5) = O s(5+2) (5+3)²

A: F(s)=10s(s+2)(s+3)2

Q: T Find the average value of the function f(p, 0, 0) = pcos over the solid upper ball p≤1, 0≤ ≤ 2.…

A: fρ,ϕ,θ=ρcosϕ

Q: Solve the following equations in the interval [0, 2*]. Note: Give the answer as a multiple of x. Do…

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Q: (A) Find the maximum revenue. (B) Find the maximum profit, the production level that will realize…

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Q: Here and method M₁ = tano = y M₂₁₂ = tand ₂ So tano = 0 O = 4 25 4-04 1 +1-6 tan" (1.3846) 154.16…

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Q: Complete parts a through f below to find nonnegative numbers x and y that satisfy the given…

A: x+y=63P=x2y

Q: Write the equation for the plane. The plane through the points P(5, -3, 10), Q(-3, -2, 29) and R(-1,…

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Q: Evaluate the triple integral. JIJ 2x dV, where E is bounded by the paraboloid x = 5y2 + 5z² and the…

A: ∫∬E2xdV , x=5y2+5z2  and  x=5

Q: a) y' - 2xy = x b) y' + sin(x)y=sin(x)

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Q: Compute the right-hand and left-hand derivatives as limits and check whether the function is…

A: Checking the differentiability at point P.

Q: Using implicit differentiation, find Provide your answer below: dy dx - 4xy³ - 6xy² =

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Q: a. Find the open interval(s) on which the function is increasing and decreasing. b. Identify the…

A: ⇒gx=x3-3x

Q: Which of the following statements about the series A B The series diverges by the nth term test.…

A: We have slove above question

Q: a) Find the first and second derivatives. f'(x) = f"(x) = f(x) = x³ -4.5x² – 12x - 3 b) Identify the…

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Q: Let T: R² → R² be the linear (matrix) transformation defined by: T(₁, ₂) = (2x1 − 5x2, 9x1…

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Q: Perform a first derivative test on the function f(x) = -2x²-3x+5; [-4,4]. a. Locate the critical…

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Q: Determine the point where the lines x = 4t + 1, y = t - 9, z = 2t + 1 and x = 5s + 1, y = -s, z = 5s…

A: The given lines are:L1:    x=4t+1,   y=t-9,   z=2t+1L2:    x=5s+1,  y=-s,    z=5s-9

Q: Use cylindrical coordinates. (a) Find the volume of the solid that the cylinder r = a cos θ cuts…

A: calculation of above requirement are as follows To find the volume of the solid that the cylinder r…

Q: 8. The nth-Term Test can be used to determine divergence for which of the following series? 1. (A)…

A: nth term test If limn→∞∑n=0∞an=L then series divergers. Where, L is any arbitrary value except zero.…

Q: y + 7y=0 y(0) = −2, y'(0) = −3 nd the equation you get by taking the Laplace transform o e…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, and y are positive.…

A: The function is given by fx, y = x2-10x+y2-14y+28 The constraint equation is x+y = 18…

Q: A child flies a kite at a height of 50 ft, the wind carrying the kite horizontally away from the…

A: We have to find rate of change of the string of kite to goes away from child.

Q: Evaluate the triple integral. JIL 4z dv, where E is bounded by the cylinder y2 + z² = 9 and the…

A: The area E is bounded by the cylinder y2+z2=9 and the planes x=0, y=3x, and z=0 in the first octant.

Q: Use the Fundamental Theorem of Calculus to evaluate (2/t − 2) dr.

A: We are required to find: ∫-11t3-2dt

Q: Find the maximum sustainable harvest of the given function. f(S)=24S where S is measured in…

A: We have to find maximum sustainable harvest.

Q: Find the function f given that the slope of the tangent line to the graph of a dily appropriate.)…

A: Slope of tangent line is f'x=ex+3x

Q: MV -1 -2 -3- (a) List all intervals where fis increasing and decreasing. (Enter your answers using…

A: Function is increasing in the interval where value of derivative graph positive and Function is…

Q: 6. If P (t) = 2 sin t, then find P(19) 2πt 3

A: given P(t)=2sintwe know  d dt(sint)=costd dt(cost)=-sint

Q: Since YouTube first became available to the public in mid-2005, the rate at which video has been…

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Q: 6. Let f: R→ R be any continuous function such that f(x + y) = f(x) + f(y). If ƒ(7) = 4, find f ¹…

A: We are given that f(x+y)=f(x)+f(y) and f(7)=4.

Q: Find the particular solution of the differential equation y""-3y" + 4y = 6+80cos2x, y(0) = y'(0) =…

A: The DE is given that , y'''-3y''+4y=6+80cos2x , y0=y'0=y''0=0 find the particular solution.

Q: Find the derivative of y with respect to x. dy dx y = 6 In 11 5 X

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Q: (c) A rectangular box with a lid has a volume of 60 mm². The length of the box is three times the…

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Q: A body moves on a coordinate line such that it has a position s = f(t) = Mic Nuuy ο κιμiaUGITICIIL…

A: We have to find the displacement speed and acceleration using the given position equation

Q: Find the value or values of c that satisfy the equation f(b)-f(a) b-a of the mean value theorem for…

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Q: Determine if Rolle's Theorem can be ap- plied to f(x) = x²-3x - 18 x 9 on the interval [-3, 6], and…

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Q: 7. aluate the double integral. W x² + 1² CC = {(x, y) | 0≤x≤ 4,0 ≤ y ≤ √x} 21.

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Q: 6) Find the derivative of f(x,y,z) = xy² + yz at (1,1,2) in the direction of the vector A = 2i-j+2k.

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Q: Evaluate the integral. 2 √√Z T SSS (² cos ²0+z²)r de dr dz 000 2 √√Z T SSS ² cos ²0+z²) r de dr dz =…

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Q: Problem 3. Compute the following integrals. 2√√/22-22 V 1. √ √ 5√2²2² + y²dydz

A: Note:-Since you asked multiple questions ,according to our policy we can solve only first question…

Q: Solve the logarithmic equation. Inx+ Inx² = 24

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Q: Consider: f(x) = x² ln (x) At which a-value(s) do the local maxima/minima occur? (Hint: Because of…

A: The given function fx=x4lnx. We have to find the critical points of the function. Use the derivative…

Q: го Find the eigen values and eigen vectors of the matrix: A = 1 Lo 1 0 -27 3 0

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Q: Describe the line in coordinate form in space passing through the points (6, 4, 3) and (8, 7, 1…

A: we have to find the line equation in the space which passesthrough points P(6,4,3)    and  Q(8,7,10)

Q: Find the area of the shaded re

A: here , we have graph  of  shaded part ,    then we have to evalauate  the area  of shaded part

Q: Write the equations in cylindrical coordinates. (a) 4x²9x + 4y² + z² = 7 (b) z = 9x² - 9y² X

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Q: Maintenance costs for buildings increase as the buildings age. If the rate of increase in…

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Q: Use linear approximation, i.e. the tangent line, to approximate 2.6³ as follows: Let ƒ(x) = x³. The…

A: Let fx=x3 The equation of the tangent line to fx at x=3 can be written in the form y=mx+b…

Q: Find the present value that will grow to $23,000 if interest is 6% compounded quarterly for 17…

A: The solution is shown in step-2

Q: Let s(n) *(1 + ² )(²). Find the limit of s(n) as n→ ∞o. . n

A: