Differentiate the following, and simplify: a) y = x'e* b) f(x) = 2" + 7** evi c) g(1) = 1+ev

Q: hi

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Q: y" + y" – 4y' – 4 = 8x + 8 + 6e™

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Q: Solution

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Q: Sixth derivative of a sixth degree polynomial is a line. Select one: O True O False

A: Given : Sixth derivative of a sixth degree polynomial is a line. To find: State whether the above…

Q: determine which statement is true {(x, y)|x = y2} (A) not a function (B) function; domain: R (C)…

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Q: What are all values ofk for which x'dx = 0?

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Q: ield F = (A, B, C) such that A = 2zx, B = 3z + 2y, 0,0,0) = 1 and C is independent of

A: We have to find the following conditions according to the given information

Q: r(0) = tanh-1(cos 0) + cosh(0º)

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Q: 3 (-4V3,-2V3) :44. V=

A: Vector

Q: Find the nth derivative of y = In(16x2 – 9).

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Q: j(r) = e sech

A: The given function,      jr=esechr2+2r

Q: Which of the following Cartesian equations is equivalent to the polar equation T= 4 cos 0? Select…

A: We can convert from polar to cartesian equation as below.

Q: Let, \(f(x)=4x^2-12x+10\). Find: (a) the x- coordinate of all critical points, b) the open intervals…

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Q: The function g(t) = (8t)t – cosh? t + sinh? t satisfies gʻ(c) = 0 for which value of c?

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Q: 1. Find the derivative of the following: (Simplify your final answers.) sech h. j(r) = e (Using…

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Q: d 31. Evaluate et ht dt 1 ((1+ Int) dx 1 A) x(1 + Inx) C) x+1 xe* B) 1+x D)

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Q: y² = csc*5x cot°sx aS C

A: Here, the given function is: y2=csc25x cot25x⇒y=±csc 5x cot 5x...(1)

Q: Find all the derivatives of f, given f(x) = x3 - 5x' + 4x6 – Tx* + 3x3 + 11.

A: This is a basic derivative problem

Q: 3. Find the integral * dx a² -2 x+1 a.-x - - x - In(x + 1) + C 2 b.x2 – x – In(x + 1) + C c.x2 – x +…

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Q: 2. Write down the name of the conic given by the polar curve r = 6/ (3 - 2 cose). Determine the…

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Q: ||r'(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). 13 r(t) = t'i+5j 390 t14 K(t) = %| (4…

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Q: Find two positive numbers satisfying the given requirements. The sum of the first and twice the…

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Q: 1. Consider the curve C with parametric equations Sx(t) = t3 – 3t +1 lu(t) = t(t +1) defined for t e…

A: Given information:  xt = t3-3t+1yt = tt+1               , where t∈ℝ.…

Q: Question 3 How much work is required to pump all the water from a right circular cylindrical tank,…

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Q: What is the probability you draw two cards of the same color from a standard 52 card deck you are…

A: we know that  The deck has cards in two colours red and black

Q: d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly…

A: ddtr1(t).r2(t)=r2(t)dr1(t)dt+r1(t)dr2(t)dt ddtr1(t)×r2(t)=r1(t)×dr2(t)dt+dr1(t)dt×r2(t)

Q: Let g be a function with derivative given by x2 - 2x - 8 g'(x) = V2x³ +5 - 1<x <5 %3D . At which…

A: Occours

Q: A conical surface is defined as 0 = 30°,0 < y< 2n,0<r< 2, the lateral surface area is what?

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Q: 4- The number of element in the sample space when you flip 3 coins together c) 6 d) 12

A: We can solve this as follows:

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

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Q: 37. v = (60, 11}

A: Unit vector n→ in the direction of a vector v→ is given by, n→=v→v→, where v→ is the length of the…

Q: A ball is thrown vertically upward from the top of the house 112 ft high with an initial velocity of…

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Q: Q3.4:Choose the appropriate answer: 1-If P(A)=0.7 ,P(B)=0.2, P(AnB) = 0.5,then P(A U B) = c)2 a)0.6…

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

Q: In(x² + 1)dx

A: We can solve the integration as below.

Q: 19x + 900 The average cost for a company to produce x units of a product is given by the function…

A: To find change in average cost as production goes from 150 to 151 units.

Q: The reverse order of 6 k 3xe" dydx is equal to 2 2(e - 1) O e - 2 O -e

A: Given: I=∫02∫x213xey3dydx The region bounded by the curves y=x2, y=1 from x=0 to x=2

Q: Using Optimization in Derivatives, solve the following question: A farmer wants to have small garden…

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Q: determine which statement is true (A) Not a function (B) Function; domain: R (C) Function;…

A: This is a function problem

Q: . [ID # ending in 4 or 7] a?v if v csch y = e*². dv Determine ( + ду. ax дх ду

A: Here, the given function is: v csch y=ex2⇒v=ex2csch y⇒v=ex2sinh y

Q: 3 The triple integral L (x + 2y – z)dxdydz is equal to

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Q: 3. Find the volume of a solid of revolution generated by revolving the region under the line 2x +1…

A: Volume of solid = integration of πf(x)^2 dx from x1 to x2

Q: III. Find the area of the regions bounded by the curves. Draw a figure showing the region. 8. y =x;…

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Q: (a) Consider the system of equations 11x3 – 3x1 7x — бх2 — 5хз x2 +2x3 – 2x1 = yi = y2 - Уз Rewrite…

A: To write the system of equations in matrix form

Q: Vx-5 1) Evaluate lim 10. x+25 X-25 Show every step.

A: We can find the limit as below

Q: is the graph a function?

A: To determine whether the given graph represents a function.

Q: 16) Rewrite the integral 10 3(1 – z/10) 7(1 – y/3 – z/10) dx dy dz in the order dz dy dx.

A: To rewrite the integral ∫010∫031-z10∫071-y3-z10 dx dy dz in the order dz dy dx

Q: A ball is thrown vertically upward from the top of the house 110 ft high with an initial velocity of…

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Q: Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, from the…

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Q: 3 S(x) = 6x² + x – 7 Find the coordinates of the point of inflection on and prove that it is a point…

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Q: Which of the following is the Taylor series expansion of the function (x) =ex? with center at 0. 00…

A: Taylor Series representation of e-x about x=0 is given by, e-x=∑n=0∞-1nxnn!....(i)