can you explain the whole process, step-by-step? like in an essay type. how did they find the first and second derivatives?

Q: Find all critical points of the function f(x) = x³ - x? – 54x + 6. (Use symbolic notation and…

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Q: If f(x) = 6 sin- (x), then f'(x) =

A: We have to find solution

Q: 1-50 of 1,223 Systems 5:51 PM 11. Consider the matrix (PDT) (thoke@pdx.edu) - Y.. 4:43 PM 1 -…

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A: The figure inscribed in the sphere is needed to be maximized. So, volume of cylinder is to be…

Q: Evaluate the definite integral: – 1| dæ

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Q: 8. Determine by the ratio test if 2n=1 (2n)! converges or diverges.

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Q: Given the following functions: f(x) = cos(x) g(x) = x" + 1 Find f(g(x)) and (f(x)). (Use symbolic…

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Q: Find the general solution of the following differential equation: (sin x)y' + (cos x)y = ex Then…

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Q: question

A: We will solve the second problem.

Q: The slope of the graph of the function y = 2x at (32,8) is %3D Tuno n mplifGed fraction

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Q: Nse Ithe me tsodl undetermined Cofficients to solve Ithe diffevential equation dy +ay = cos bx ¥a…

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Q: f(x) = In(1 + x5) %3D f(x) = Σ n = 1

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Q: Fine the area of the surface obtained by the rotating the following curve about the x-axis. (The…

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Q: Find the indefinite integral. Hint: Let u = 5- Vx. (Remember the constant of integration. Remember…

A: To evaluate the given intgral.

Q: Find the function F that satisfies the following differential equations and initial conditions.…

A: We will find the function.

Q: of of and ду For the function f(x,y) = In (7x+y), find of af ду II II

A: Solve the following

Q: メyゴ= ザ+×x。+y %3D ind gen eral solution

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Q: Find the linear approximation of f(x) = sin x, for x close to 0

A: The given function is: f(x)=sin x To find the linear approximation of it close to 0.

Q: Evaluate the integral. 1/3 6 sec x dx 0. n/3 2 6 sec x dx %3D 0.

A: To find out the integration.

Q: / (22* + 3,/5 +) Calculate the indefinite integral: dz

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Q: f(x) = cos(x) g(x) = x' + 1 Find f(g(x)) and g(f(x)). (Use symbolic notation and fractions where…

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Q: farmer finds that if she plants 55 trees per acre, each tree will yield 35 bushels of fruit. She…

A: Given query is to find the number of trees to be planted per acre.

Q: 1) Find the absolute maximum and minimum values offon the given closed interval, and state where…

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Q: Determine whether the function is continuous at the given points. x+2 if x22 : 2,0 x if x<2 f(x) =…

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Q: 135 5. y = x³, y = x + 6, and 2y + 2 = 0 (Answer: S. u.) 4

A: The region bounded by the curves y=x3, y=x+6 &amp; 2y+2=0 is:

Q: 72-1 b) En=1an for an 5. )** 00 %3D

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Q: g integral. dx

A: Given query is to find the value of the integral.

Q: Find the equation of the tangent line to the curve y = e' when it is paralel to 2r-y =7.

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Q: Use the substitution u =x + 1 to evaluate the indefinite integral below. 5 1) dx Write the integrand…

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Q: 1 7. Determine by the ratio test if n- converges or diverges. п! -

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Q: 3n3-2n2+4 6. Determine by the limit comparison test if Ln= n=D1 converges or diverges. n7-n3+2

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Q: Find the derivative. dx dx

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Q: 4 -4 -3 -2 -1 1 2 3 4 5 -2 -3 -4 -5 The plot above is created with the parametric equations Sæ(t)…

A: From the graph we can see that in horizontal direction the maximum value is 6 so, a=6. From the…

Q: Solve the equation (x^4 + 2y)dx - xdy = 0

A: I am attaching image so that you understand each and every step.

Q: 1) Find the explicit formula of an arithmetic sequence with the given property. d = 12, and a6 = 68

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Q: 2) Find the absolute maximum and minimum values of f, if any, on the given interval, and state where…

A: We know that for absolute maxima and minimum value we do derivatives. We know that derivatives of…

Q: te: sec(5 x + 4) tan(5 x + 4) dæ

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Q: 1. The position of a particle is given by the function s(t) = t* – 32t where t is measured in…

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Q: 6 sin(x)dx

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Q: Find the area of the parallelogram that has two adjacent sides u = -2i + 4k and v =i +2] +k Axn pu…

A: We will find the cross product and area.

Q: Solve 1Ge follouing disferential eguatiug 2 dy ty= elx xy メー1

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Q: Ing light is located 10 feet from a wall. The light completes one rotation every 3 seconds. Find the…

A: From the given data: Here, the complete 2π rotation is done in 3 seconds.  So, dθdt=2π3 rad/sec

Q: 1 13 + x xp-

A: We will solve the integration.

Q: Find the minimum and maximum values of the function y = 1613 + 2412 on [1,2] by comparing values at…

A: The given function y=16t3+24t2 on 1,2

Q: 12. Solve the second-Order differential equation: d²y - y = e* (use method of variation of…

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Q: Use the Laws of Logarithms to expand the expression. 4x7 In (x + 3)8

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If 7+ 2n2 an…

A: We have to find out limit

Q: For the following table, assume that y = a (x ^b). Then 2 7 9 11 11 17 13 25 y = 3.083 x^2.312 O…

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Q: yA C(0, 1) B(1, 1) y = Vx R2 R3 y=x³ %3D A(1, 0) Referring to the figure above, find the volume…

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Q: 8. Given, h(x) =2 – x and g(x) = -x² + 4 a) Plot the two functions on the same graph for -2 < x <4…

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