Using integration by parts and taking a > 0, the integral x In(ax)dx is equal to: In a 2 In(2a) - 3 In a 2 In(2) - 2 3 3 4 the above the above

Q: O Use the divergence theorem to evaluate F-dS, where F (x, y, z) = zxi – e"j+ 4zk and S is the surfa...

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Q: Consider the following vector field F (x, y, z) = yz cos (xy) i+ xz cos (xy) j+ sin (xy)k (a) Use th...

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Q: The function A Age0.19t models the amount an individual owes a credit company t years after some ini...

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Q: Given revenue and cost functions R(q)=80q−0.2q2 and C(q)=15q+500​, find the quantity that maximizes ...

A: This question can be solved using the concept of maxima and minima.

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

A: Here we have to find the unit vectors.

Q: Use the First Derivative Test to find relative (local) maximum points or minimum points, if any, of ...

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Q: 15. (ez + e-z)2 dx.

A: Given: I=∫01ex+e-x2dx As we know from the hyperbolic trigonometric identities; 1). sinhx=ex-e-x2 2)....

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Q: 6. y = In (e' + e")

A: The given problem 6 is solved below in detail.

Q: To evaluate the integral 4+2a dr, we use Select one: O Substitution with a = 2 sin 0, where Substitu...

A: Given :∫4+x2dx

Q: 2. Evaluate lim -4x+1 X-1 x-1

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Q: C. Optimization 1. Use the first derivative test to determine the relative extrema of the following ...

A: The given function f(x)=x2x-22

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Q: Verify that the series Σ n +1 n=1 satisfies the conditions of the Integral Test, then use the Integr...

A: The given series ∑n=1∞nn4+1

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Q: 7) An open-top box is constructed from a piece of cardboard 50 cm × 40 cm by cutting congruent squar...

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Q: In how many ways can John, Leo, and Mike be seated in a row? a. 3 b. 4 c. 5 d. 6

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Q: If 0 be a positive acute angle satisfying cos² 0 + cos“ 0 = 1 then the value of tan² 0 + tan“ 0 is

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Q: Obtain the particular solution satisfying the initial conditions indicated.

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Q: +00 S" x?dx

A: To write that the given integral is improper or not.

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A: We have to write the definite integral for the volume

Q: Use the price-demand equation below to find E(p), the elasticity of demand. x= f(p) = 9600 – 6p- ......

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Q: Consider the function f(I)= 6x +5x. For this function there are four important open intervals: (-0, ...

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Q: dy 2y + cos dx ||

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: Determine whether the definite integral converges or diverges and evaluate it if it's convergent im...

A: ∫0∞ xx+1dx

Q: cos2x – sin2x cos2x For -dr =-F(x)+ C• What is F(x)? cosx - sinx A sinx – cosx) - B 2 sinx + -cos'x+...

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Q: 2 + x², -2 <x< 0 1. f(x)dx; f(x) = -x + 2, 0<x<4 -2 2

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

Q: 2. Find the slope of the tangent line to the curve f (x) = -1 2 at x

A: Given: f(x)=2x

Q: Determine whether the given series is convergent or divergent. +oo 5n + sin? Σ - | sin n| а. 3" n=1 ...

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Q: Write an equation for the function graphed

A: Given graph:

Q: Evaluate the integral: el/z dx -1

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Q: Choose among the following tests ONLY: integral, comparison, and limit comparison to determine if th...

A: We have to check weather the given series is convergent or divergent

Q: 21n|sinh (1/2 »)|+C

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Q: Sketch the level curves of the function f(x, y) = y – 3x² for c = 2. 8+ 5- 4 2 -6 -5 -4 -3 -2 -1 4 -...

A: Explanation of the answer is as follows

Q: (1) ydx + (x + 3y²)dy = 0

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as th...

Q: 2nd deivative vong impliat dipperentiation x'y +y*x = X. -2

A: We can find the 2nd derivative of the given expression as below

Q: Determine the values of a, b, and c such that the cubic function f(x)=ax^3+ bx^2+ cx satisfies all o...

A: Given problem:- Determine the values of a, b, and c such that the cubic function f(x)=ax3 + bx2 + cx...

Q: Solve the inequality. x-2 < 0 X+1

A: Given,            x-2x+1&lt;0

Q: (1.5,2) 1.5 (0,7, 0. 2) f0.7,02) O5 ー15 -05 O.5 0.5 1.5 1 -0.57 (ーム2,-) -15: -2 Where does f have lo...

A: From the given graph we can see that- f has local minimum at x = 0 and x = 1

Q: Evaluate the limit. 2x5–16x² lim→2 2.2+ a³

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Q: has

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Q: The integral is equal to 2e + C. Select one O True O False

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Q: 10. x= cost; y = sin't

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Q: Use the First Derivative Test to find relative (local) maximum points or minimum points, if any, of ...

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Q: Let {an}n=1 be a convergent sequence such that a1 = v5 and an+1= /5an Compute lim an

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Q: Find the absolute maximum and minimum of f(x,y)= 4xy^2 - (x^2)(y^2) - xy^3 on the closed triangular ...

A: f(x,y)=4xy2-x2y2-xy3fx=4y2-2xy2-y3fx=04y2-2xy2-y3=04-2x-y=0 ...(1)fy=8xy-2x2y-3xy2fy=08xy-2x2y-3xy2=...

Q: Consider the function f(x) 4x +4x 8. f(x) has a critical point at 2 = A. Find the valtue of A: A = A...

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Q: 7. Let C be the curve y = 3x for 0 <x S 1. 0.5 Find the surface area of revolution of C about the x-...

A: Given: y=3x3 for 0≤x≤1

Q: 9 y= Arctan( 1-2x

A: Use simple differentiation twice to get the answer.