Evaluate the function. If the value is not a rational number, round your answer to three decimal places. coth(ln 7)

Q: 20 Q41. Term independent of x in expansion of is? бх3

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Q: S- dy - = 2/y- 5in|Vy+ 5| +C Vy +5 А) True B) False

A: ∫dyy+5Let y+5 =xdifferentiating on both sides12ydy=dx=∫2y dxx=2∫x-5xdx=2∫(1-5x) dx

Q: Evaluate the following limit using Taylor series. lim 2x X00 ... Rewrite the given limit using a…

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Q: Use two iterations of Newton's Method with initial guess xo = to approximate the solution of f(x) =…

A: We have to find the value of x2.

Q: Evaluate: e* cos (7e*)cos (4e*) dx (A sin (3e*) +sin (11e") +c - sin (11e*)+C - sin 6. 22 ® -cos…

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Q: each of the problems, solve the given differential equation. 1. y` = x2/y

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

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim +00\ 5t2 + 6' 6t (?, ?)…

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Q: Select as many answers as possible. * Find the absolute extrema of the function 2/3 f(x)=(x+1)* in…

A: f(x)=(x+1)(2/3)    ,    [-2,1] f'(x)=2/3(x+1)(-1/3) At critical points f'(x)=0 2/3(x+1)(-1/3) =0…

Q: A man 6 ft tall is walking at the rate of 3 ft/sec toward a streetlight 20 ft high. At what rate (in…

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Q: Question 11 |In |25- x² -dx , if we let u=V25- x² , then udu= - xdx. T True F False

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Q: x2 In solving for the antiderivative of f(x) = Fusing trigonometric substitution, Jf(x)dx is V4- x²…

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Q: Evaluate: | sech[In cosx]tanx dx A -2 tan -1(e cosx) +C В -2 tan -1(cosx) +C 2 tan -(ecosx) + C (D 2…

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Q: 5. S csc* dx *csc4 x²

A: Given problem:-

Q: x² + 64 Using trigonometric substitution, given - dx, the simplified form of the integral is: (sec…

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Q: (1) Evaluate the triple integral I zyz dV, R where R = {(z, y, z)| 0 < z < 3, -2 <y< 1, 1< z < 3}.

A: We will use simple Integration rules to solve this triple integral.

Q: Given In.ry+x+ y =2. Find dy by implicit differentiation. dx

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Q: | sinh54x cosh 4x dx can best be evaluated by General Power Formula. A True В False

A: Option A is true

Q: Write Tif the statement is true, or F if it is false. Write your answers on the blanks. dx x +C 3 2.…

A: 1.∫5x233dx=∫53x23dx=53x5353+c=x53+c1. T2.∫-45x544dx=-45x944×49+c=-5x94+c2. T

Q: :Q: solve the following equations 2X-3Y+Z=-1 X+4Y+5Z=25 3x-4y+Z=2 x=8.7 y= 5.7 z= -1.3

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Q: A line with positive slope passing through (-1, 1) and intersects the parabola y = x² at the point P…

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Q: In x2/25+ x² dx , we let x= 5sine. T True F False

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Q: Using trigonometric substitution, given (Vx+64 dx, the simplified form of the integral is: sec³ed®…

A: We have to check whether the given statement is true or false.

Q: 3 3 25x ? 2 7x3 3 16х5 dx 5

A: use property of integral to solve this.

Q: Q38: If y = e2x sin 5x, then which of the following is true? (a) y" – 4y' + 30y = 0 (b) y" – 4y' +…

A: Given,            y=e2xsin5x

Q: 00 n8" Use the ratio test to determine whether>. converges or diverges. (n + 1)! n=7 (a) Find the…

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Q: S sin®xdx

A: ∫sin6x dx       We have sin2 x=1-cos2x2 Then ∫sin6x dx=∫sin2 x3dx                  =∫1-cos 2x23dx…

Q: 3. Use the surface integral is Stokes' Theorem to calculate the flux of the curl of the field F…

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Q: dz ins- , if we let y=Vz+4, then the new integral becomes z+4 -2 у-2 True B False

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Q: | Find the minimum point for the function f(x) =1 + 12x – 4x (2,-7) (0, 1) Oa.9) (1, 9) O (-1, -7)

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Q: nd derivative of f(x) = x In(x)

A: We have to find the second derivative of the given function

Q: Find the derivative of f(x) = x In(x) 1- In(x) O In(x) O1+ In(x) O In(x) /x

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Q: ey -2Vy-5inlVy+5| +C Vy+5 A) True False

A: I = ∫dyy+5 Let, y = t2   ...(1) Differentiating both sides, gives dy = 2tdt  ...(2)

Q: dx Evaluate: x/9x2 + 4 None of the above V9x2 + 4 + 2 In 4 f (x) = +C © f(x) = -2ln V9x2 +4 + 2 + C…

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Q: Give the VALUE only. No need to include the unit. * Let s, =15r +10r +20 and s3 = 5t + 40f , t 2 0,…

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Q: The antiderivative of [Vx²-25 dx is x2 – 25 – sec-lx+ C. A True B) False

A: ∫x2-25xdx

Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

A: Given that the tetrahedron enclosed by the coordinate planes and the plane 7x+y+z=4.

Q: (1 f(x) ={ 5 if x = 4 at x = 4 if x + 4 x - 4

A: limit continuity differentiability at x=4

Q: Find if yvx – 8 = xy + 2.

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Q: Sketch the region of i nd change the order of integration ntegral 9. 3 f(x, y) dydx

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Q: 3 3. Given the graph of the function ƒ(x)= (x+2) a. Give a step-by-step explanation of how to graph…

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Q: 1. Use a parametrization to express the area of the given surface as a double integral and then…

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Q: x² + 64 Using trigonometric substitution, given -dx, the simplified form of the integral is: x2 sec³…

A: Given: ∫x2+6464dx

Q: Reduction of order can be used with 2x to find a second solution for the %D DE: 2x²y" – xy' - 2y =…

A: Given y1= 2x² is a solution of 2x²y''-xy'-2y=0....(i) So 2x²y1''-xy1'-2y1=0....(ii) Let y=…

Q: The auxiliary equation of the DE: -6 y"" -4 y" + -2 y=D0 is -6 m3-4 m2 +-2 0. Select one: O True O…

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Q: Question 11 a / f(x) dx: f(x) dx a True False Question 12 If f'(a) = 0, then the function f must…

A: Here we have to use the concept of integration and derivatives.

Q: Determine a region whose area is equal to the given limit. Do not evaluate the limit. 11 lim 3 + n-…

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Q: Work Problem 1 (With integrity statement] ( Let R be the region bounded by y-x+2, y=0, and x=2. Draw…

A: Given; I=∫∫R-2ydA And y=x+2, y=0, x=2   As we know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C And…

Q: DO NOT include spaces in between characters. * Using implicit differentiation, find the slope of the…

A: We can solve this as follows:

Q: 8:44 C ing e Determine whether the series is convergent or divergent. 00 1 n = 1 The series is a…

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Q: Prove the product rule of differentiation.  That is prove that if p(x)= f(x) g(x), where  f(x) and…

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