L, f(x)dx + [° f(x)dx = 5. Si f(x)dx – Sº f(x)dx = 4.

Q: 2. y = [log(arccotx³)]coshx. Find dy/dx

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Q: -2 2. S- dx x(x-1)

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Q: P1. 18. Which of the following is true? Select one: O a. AxB is the same as BxA O b. If vector A is…

A: Vector

Q: Refer to the given below. Find the indefinite integral. Simplify your final answers (Just like how…

A: i)∫(2x3+12x2-5)dx=∫2x3dx+∫12x2dx-∫5dx                                   =2∫x3dx+12∫x2dx-5∫dx…

Q: 1+tan-1x D. y = + sec-1xcsc¯1x + xsin-1x +V1 - x2 2-3tan-1x

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Q: integrate dx/(x²+x)(x-1)²

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Q: 2 x – 4 dx .2 1

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Q: 22. u = Vr² + s², r = y + x cos t, s=x + y sin t; ди ди ди əx’dy when x = 1, y = 2, t = 0 dt

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Q: Evaluate the following indefinite integral: x dx 1.) S- Vx4 - 1

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Q: 1+2x2 dx J x2(1+x?)

A: A detailed solution is given below

Q: 3. y = In? (csc2x). Find y"

A: y=ln2(csc2x)

Q: testconuer gnce and diverg ence 2+5 3"

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Q: integral of 3/(x^2)+9

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Q: 2. Find the Area bounded by the curve y=4-x2 and the x-axis.

A: 2. The area bounded by the curve y=4-x2 and the x-axis Note:    Multiple questions are given, we are…

Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 4 sin(x). If f(0) = 2 and f'(0)…

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Q: 8 f(x, y) = y/x, P(1,2), u = }(2i + 5 j) |(2i + /5 j)

A: To find the gradient at the given point and then rate of change for the given function.

Q: Integral

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Q: Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x2 b.…

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Q: Use Lagrange multipliers to find the extreme values of the function f(x, y, z) = x² +y? + z2 subject…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: 3 + In?x dx

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Q: d Calculate r1(t) · r2(t)] and dt d [ri(t) × r2(t)] first by differentiating the product directly…

A: Given that,       r1(t)=9t i+4t2j+5t3k,   r2(t)=t4k

Q: Find the following for the given equation. r(t) = 8 cos(t)i + 8 sin(t)j (a) r'(t) = (b) r"(t) = (c)…

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Q: Evaluate the integral. V3 8 dx /1/v31 + x

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Q: A particle moves vertically (in inches) along the yaxis according to the position equation s(t) = -…

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Q: C. y = cosh¯'(x² + 1) + tanh-1(sinx) + sinh-'(cothx²)

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Q: A ball is kicked such that its height (h) can be represented by the equation h = - 16t2 + 64t + 9,…

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Q: A forest has a population of cougars and a population of rabbits. Let æ represent the number of…

A: We will solve the given differential equations with condition

Q: 1. Find all relative extrema and saddle points of the functon Use econd Partials Test where appli…

A: In given problem we have to find out relative minimum of given function for which first we find out…

Q: The marginal cost for a company to produce q items is given by MC(q) = 0.002q -0.7q +620. The…

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Q: y= e. tan ba Solve for y where a and b are constants. Express you

A: Solving

Q: Find the arclength L(C) of the helix C parametrized by C: r(t) = (2 cos t, -3t, 2 sin t) for 0 <t <…

A: The arc length of the parametric curve is given by: ∫ab(x'(t))2+(y'(t))2+(z'(t))2dt...(1); a≤t≤b…

Q: 2r-4x2-x-3 dx x- 2r 3 In Ix+ 1 +3 ln|x-3| + C +1-3 ln|x-31+ C Option 1 Option 2 2 In |x + 1| - 3…

A:

Q: An archaeologist found a burial jar when excavating in an ancient village. To determine the age of…

A: Rate of decay of C14 is proportional to its amountdctdt=kct…

Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

A: integration

Q: Find aw/@s and dw/at using the appropriate Chain Rule. Function Values .3 W =V 4, t = 8 X = e, y = e…

A: We can solve this as follows:

Q: Given the linear differential equation: y'' - y = cos(x) - 5sin(2x) Find the general solution…

A: Solving

Q: 1 If z = 2x2 – 3y with u = x² sin y and v = 2y cos x, determine expressions %3D az dz for and du

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Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

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Q: Consider f(x) = (5x + 11)2022, find: i. f'(x) ii. f"(x) iii. f''(x) iv. fiv (x) v. f°(x)

A: Given, f(x)=5x+112022

Q: Let A = 2. Find the eigenvalues of A 3.

A: Use eigen value concept

Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

A: To evaluate the value of  ∫-∞∞7x2+4x+8dx=7∫-∞∞7x2+4x+4+4dx=7∫-∞∞7(x+2)2+22dx

Q: 1 2 f(t) = 3 Vi+1 2. Given SET A. determine f"(t)

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Q: k=0 X n-1 The sequence { Xn}, where n20, is defined by Xo = 1 and Xn= E (xx) for n 2 1. The infinite…

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Q: Find the unit tangent vector T(t). r(t) = t2i + tj +4k , P(9, 3, 4) T(3) = Find a set of parametric…

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Q: Find the directional derivative of the function

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Q: [1 1 1] Suppose we have a matrix A= |1 0 1 2 1 2 What is rank of A?

A: GivenA=111101212R2→R2-R1R3→R3-2R1A~1110-100-10R3→R3-R2A~1110-10000We know that The rank of a matrix…

Q: Find y': y = arctan(e2x) 2e2x y 1– e4x? 2e2x y = 1 – e4x %3D 2e2x y 1 + e4x %3D 2e2x y 1 + e4x2

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Q: Question 2 Determine the derivative of sec(x) tan(x) O sec z + sec z tan? x 2 sec? z tan x sec x O…

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Q: 2 X+ 9x + 2 x3 +2x? -x - 2 dx

A: