) Eliminate the arbitrary umstants of y= C, + C2 e ** + C3 e 3x

Q: Find the equation of the line tangent to f(x) = cos² x – sin²| %3D at x = 6

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Q: x=t² +3t +5 Determine the arc – length of the curve: y = (2t- +2

A: solution:-given curve x=t2+3t+5y=232t+43/2+2dxdt=2t+3dydt=22t+4

Q: dx Vx-4x-7 S- -dy y2-8y+5

A: The given integrals are' 1)1/sqrt(x2-4x-7)  2)7/(y2-8y+5).

Q: Prove the following identity: 1- tan? e cos 20 = sec e

A: solution:-cos2θ=1-tan2θsec2θ RHS=1-tan2θsec2θ        =1-sinθcosθ21cosθ2,      ∴tanθ=sinθcosθ &…

Q: Evaluate S.(x + y)dxdy by reversing the order of integration.

A: answer is in next step

Q: 2) w = 2yTan(2x + y) – 3xSec(x²y³) %3D

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Q: Write the equation of a sine function that has the following characteristics. 1 Amplitude: 2 Period:…

A: Sine function :  y= a sin(bx-c) ; where, 'a' is the amplitude and 'c' is the phase shift .…

Q: 2. The integral S,n(4 - y²)?dy represents the volume of a solid. Sketch the region, rectangular…

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Q: Sin'e+ 3sine - 4

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Q: (D² + 4)y= 4 cot 2x

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Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (- 3, 4, 3), Q = (6, 6,…

A: .

Q: YA x= y² – 4y (-3, 3)- x= 2y – y²

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Q: Find the slope of the tangent line to the r=2-3cos 0 in polar coordinate at 0 =

A: Given:-r=2-3cosθdrdθ=3sinθTo convert from Polar Coordinates (r,θ) to Cartesian Coordinates (x,y)…

Q: 1. Find the lim f(x), value of f(-1). Is the function continuous everywhere? If not, where is it…

A: The objective is to solve the above question.

Q: S In(5 + Vr)dr

A: This question can be solved using the concept of integration by substitution and integration by…

Q: E2"x" 4η n 7. it. n=0

A: The objective is to find interval of convergence and radius of convergence.

Q: 8x? -x t 8 x (x² + 4) 9. b.4mx4 3m (x+4-ラ4an)tc c. qlnxf 6m (x"+4)-Arctan )t c d. 2mxt 6m Ge?+4) -…

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Q: Find the Laplace Transform of the functions e -2" (cost + 3 sin t) s + 5 s2 + 4s + 5 8 - 2 3 (s –…

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Q: 0:32:4 Consider the solid obtained by rotating the region bounded by the given curves about the…

A: Given problem:- Consider the solid obtained by rotating the region bounded by the given curves about…

Q: Find f5(x) if f(x)= 3√3x+2

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Q: Find the arc length parameter along the given curve from the point where t= 0 by evaluating the…

A: answer is in next step

Q: 5. Find the solution of the following initial value problems. F'(u) = 4cosu – 3, F(0) = 4

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Q: Compute the area enclosed by the curves. You must show your work. Express your answer as a fraction.…

A: In this question we have to find the area enclosed by the curves.

Q: x2 - x 1+ 3x? – 2x3

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: (2) Evaluate the iterated integral by converting to polar coordinates. 2 v8-yz Vx2 + y² dx dy o y

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Q: 6x? + Sx t 16 dx +2x +6 x + 3? a.Sinlat3l+; 4 Cが)返が)+c er none

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Q: Solve the system. If the system has one unique solution, write the solution set. Otherwise, deter…

A: The objectives to find the solution of the system.

Q: Find the slopes of the surface at the given point in the x-direction and the y-direction. z = x2 -…

A: This question is related to slope of surfaces, we will solve it using given information.

Q: set B: Problem #G · Find the equation of the line tangent to X = JL F (x) C) cos?x - sin2

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Q: Find term number 6 in the expansion of: (4x + 2)° . the coefficient for term number 6 = the variable…

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Q: Evaluate sin (44º) + cos (29º) using differentials. Refer to special triangles.

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Q: 3/1- The table below includes data from a study that was applied to five people to measure weight…

A: for disperesed of data we have to find median for weight 59 65 65 67 69 here odd number of…

Q: 3 Use the linear approximation to estimate Af = f(3.1) – f(3) for f(x) = I+x (Use decimal notation.…

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Q: Question 3 (a) Find the first and second derivative of the following function, in which a and b are…

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Q: - 7z - 25 Evaluate (3x + 5)(r – 1) Add Work Submit Question

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Q: set D: Problem #G Find the eauation OF the Iine tangent to F Cx) = cos? x - Sin? (x) at X 3r %3D 4

A: To find the equation of the tangent line at x=3pi/4.

Q: sin 2t sin 5t 20 s4 + 58s² + 441 None of the choices Option 3 10 1 s4 – 58s² + 441 2 s2 + 32 s2 + 7?…

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Q: a. V80.5 ; where: V81 = 3

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Q: A cross section of a nuclear cooling tower is a hyperbola with the equation y? - = 1 902 1302 The…

A: Solved below

Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ +…

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Q: 23л Find the exact value of sin 12 23л State the exact value of csc 12

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Q: csc(cot a)+cos? a sin? x dx

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Q: 16 x5+13x3+1 f(x) = V64x10+10x8+2x4 as x→ o and x → -∞. State the Horizontal Asyn

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Q: NONHOMOGENEOUS EQUATIONS: UNDETERMINED COEFFICIENTS  2. (D^2+D-2)y=2x-40cos2x Please answer this…

A: Here, the given DE is: (D2+D-2)y=2x-40cos 2x Now, to find the yh. The auxiliary equation of the…

Q: Joanne sells silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to…

A: answer is in next step

Q: Given: (6, 0, –2) and (0, 8, 0). (6,0, –2) × (0, 8, 0) = æi + yj+ zk. Find x +y+ z.

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Q: -dx x2 +9 I x3 +ar-23 ton- (특) +C a. 3 b. 1 x³ t qx + 27 tam " ) + C b*3-9*+27€an )+c C. d.늘-9x- 2구…

A: Using substitution method, integration is done.

Q: - dx +3x+3 メstx a. 14 マ tan ()"० 3. 6. 9 tam- C.12 tan-l C d. 9 tan tc e- more.

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Q: (6) Use the linear approximation of the following (Answers are to be expressed in 4 decimal places.)…

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Q: 2x S dx 4e2x –8eª +5

A: Procedure is correct but there are few errors in some of the steps.