dx x lnx√9 ln²x-1 S

Q: Applied Optimization Problem 1. You need to construct a fence around an area of 1600 ft. What are…

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Q: -4 -3 -2 -1 wo 4 -1 -2 -3 -4 -5 1 2 3 4 5

A: Slope is given.

Q: 5. y³ = 4(y + x²)

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Q: Consider the function f(x) = 4x²² Identify the locations where f has transition points. (Give your…

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

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Q: ex V1-e2x 1. S dx

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Q: 6. a) Find the critical value(s) of f(x) = x + 2sin(x) on the interval 0≤x≤ 2π 3 b) Classify each…

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Q: Evaluate the characteristic w "+k²x ²³w = 0 value of k in the following differential equation w…

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Q: Solve the DE by Bernoulli's Equation 3 1.6 y² dx - x (2 x³+ y) dy = 0

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Q: For numbers 4-5, consider a plane bounded by the curve x = -y² + y +2 and the y-axis. The…

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Q: 3. Let R be the region below bounded by the parabola y = 4 – x² and the lines 3x - 2y + 3 = 0 and y…

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Q: 4. Let z = x2 + y³, x = 2st, y = s - t2, s = u", and t = u sin w. Compute for Oz ду and дw ди

A: Let z=x2+y3, x=2st, y=s-t2, s=uw, and t=u sin w.To compute for ∂z∂w and ∂y∂u.

Q: 4 The terms of the Maclaurin series of the function f(x) = - -x are given by

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Q: Consider the matrices shown below: Find the value of K such that 4 B-B2C-13 = 5 1 10 18 18 B-¹C – 15…

A: Given B=4-102 and C=142315We know that if A=abcd then A-1=1ad-bcd-b-caB-1=18+12104=192104

Q: Show that if the function f(x, y) = ex siny + ecosx, satisfies Laplace Equation.

A: We can solve this as follows:

Q: 2x lim x-0 x²+5x

A: The given limit,      limx→02xx2+5x

Q: Which of the following conics has an eccentricity greater than 1? * 9x² + 16y² 36x +96y +36 = 0…

A: The eccentricities of conic sections are as follows. For circle e=0 For parabola e=1 For ellipse…

Q: Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x² + y² =25 and…

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Q: ff xy dx dy

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Q: Consider the R 2 − R function defined by f(x, y) = 3x + 2y. Prove from first principles that lim…

A: Let's evaluate given R2-R functions limit.

Q: Which of the following polar equations is symmetric only with respect to the polar axis (x-axis)? r…

A: We need to find the polar equation which is symmetric only with respect to the polar axis (x-axis).

Q: 4. Evaluate (x - 1)(x + 1)da using the Fundamental Theorem of Calculus.

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Q: A (-3, 2, -5) and B (6, 7, 2) are two points in R³. Determine: a) |AB| b) A unit vector in the…

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Q: Find two polar coordinate representations for the rectangular coordinate point (-√2, √6), one with…

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Q: The marginal cost function in a company is given by C' = 70 - 0.7x where x is the number of units…

A: Please see the below picture for detailed solution.

Q: Evaluate the triple integral ryd xydV where E is the solid tetrahedon with vertices (0,0,0), (10, 0,…

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Q: Evaluate the double integral Jª R where R is the region bounded by the lines y = x and y = 2 and the…

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Q: Please kindly show all working. Thnx. 1) Let f(x)=x3−3x2−9x+25. Use the derivative…

A: Given function,f(x)=x3−3x2−9x+25.We know that.Suppose that x=c is a critical point of fx then, If f…

Q: 0 ex [ 224²1 ex + 1 J-In 2 dx

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Q: 1. Solve the following equations: c) (x² - 4xy - 2y²) dx + (y² + 4xy - 2x²) dy = 0

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Q: Find the mass and center of mass of the lamina that occupies the region D and has the given density…

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Q: Find all critical points of f(x) = 3 + 12x - x² and use the First Derivative Test to determine…

A: Given function f(x)=3+12x-x2 To find critical points we need to differentiate the function f'(x)=0…

Q: in how many ways can we arrange the integers 1, 2, 3, 4, 5 in a line so that there are no occurence…

A: We use the principal of inclusion and exclusion.  For i∈1,2,3,4, let Ai ⊂Si be the set of all…

Q: 6 Use substitution to find the Taylor series at x = 0 of the function 1-9x 6 What is the general…

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Q: Suppose the position of an object moving in a straight line is given by s(t) = 5t² +4t+4. Find the…

A: Given, s(t)=5t2+4t+4We know that v=dsdt

Q: 9. (20 pts) Find the area between (bounded) by the curves y = x² + 10x and y=2x+9.

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Q: dx ylnx dy || y + 1 X 2

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Q: 7) Find the critical point (s) of f(x, y) = 2x³ + 3y² - 9x² - 30y + 12x-3. Then use the second…

A: solution is given below...

Q: If given f(3) = -1 and f'(3)=5, the tangent line to the graph y = f(x) at x=3 is y = 5x +16. (a)…

A: This question is based on finding tangent equation at a point on function.

Q: In2 fin² coshx dx

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Q: Find the point (if it exists) at which the following plane and line intersect. - 10x-3y-9z= - 19 and…

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Q: 3. y²(x + 2y) = 8

A: The Solution is dydx=-y2(x+3y)

Q: Compute for f '(3) using the limit definition of derivative if f(x) - 6x²

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Q: I. Evaluate each of the following iterated integrals. /2 siny 1. f/dxdy inx 2. ² ye²dzdxdy

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Solve the DE by Homogeneous Equation 1. x y dx + (x² + y²) dy = 0

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Q: S -1 etan 1+4t² 2t - dt

A: Let u=tan-1(2t)⇒dudt=21+(2t)2=21+4t2⇒du2=dt1+4t2 ∫etan-12t1+4t2dt=∫eudu2…

Q: The population of a small city is 90,000. 1. Find the population in 20 years if the city grows at an…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: S x-6 x²+9 dx

A: To evaluate the given integral. ∫x-6x2+9 dx

Q: 7. Determine the volume of the region that lies under the sphere x² + y² +2²=9, above the plane z =…

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Q: √35.9

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