Topic on Application of Integration - Area. Find the point/s of intersection of the graph and draw the element. Compute to find the area and indicate the formula used. Thank you!

Q: dx x3+27 8. Evaluate

A: We have to find the integral

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A: We need to evaluate :

Q: Consider the curves x = 12y? and x + 6y = 18. a) Determine their points of intersection (x1, Y1) and…

A: Given :   x=12y2 x+6y=18

Q: 1. For each of the following, find where the curves intersect, draw a sketch of the region, and…

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Q: x = -2t Given: line l1 : 3 1 – y = Z - 8 and l2 y = 2 + 2t z = 6 + 2t %3D 1. If the given lines…

A: The solution is given in the next step.

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Q: 5 sin(0) – cos(0) dO Evaluate: со

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Q: 4. Find the equation of the circle (in polar) with center on the line a = and passing through the…

A: The general equation of a circle with centre at r∘, θ∘ and radius, a is given by r cos θ-r∘ cos…

Q: Part 2. Use the integration techniques to solve for the anti-derivative of each fur I. S3p? tan p dp…

A: According to the company rule we can answer only the first question and rest can be reposted.

Q: Consider the lines x = -1+ 2s l2 : y = s z = 5+ s л — 5 3 - z l1 : 2 and I. Find two unit vectors…

A: Given

Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

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Q: A supermarket sells two brands of coffee: brand A at $p per pound and brandB at $q per pound. The…

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Q: Question 3 (a) Find the first and second derivative of the following function, in which a and b are…

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Q: set B: Problem #G · Find the equation of the line tangent to X = JL F (x) C) cos?x - sin2

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Q: I. True or False: Write True if the statement is always correct, otherwise write False. 1. All…

A: Topic:- function  Note:- as per our guideline if more than three subparts posted than only first…

Q: -2 2 dy 7e" + 5. -5

A: Given :∫-5-27ey+2ydy

Q: please

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Q: Solve the given initial-value problem y' + (tan.x)y = cos²x, y(0) = -1

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Q: Eind. the. puse..

A: power series

Q: sin 2t sin 5t S 8+3 s+7 O None of the choices O Option 1 20 10 s4 +58s2 +441 s4 58s2 + 441 Option 3…

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Q: (D6 + 6D4 + 9D²)y = 0

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Q: I. Evaluate the following integrals. 3.x5 dx V2 – x3 1. - 2* + e2" sin(2") dx sin(2") 2. 2x + 3 dx…

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Q: (c) Let f(x) = In(x + 8). (i) Find the domain and range of the function. (ii) Find the inverse of…

A: Let's find.

Q: Find two positive numbers whose product is 2 such that the sum of one number and the square of the…

A: Suppose, we take ?as a negative number having absolute value. Take a pair with the value much more…

Q: Obtain the general solution unless otherwise instructed 1. arž -y = 10sin²x dx² SUMMARY OF ANSWERS…

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Q: 4. Find (a) the gradient of f at P and (b) the rate of change of the function value in the direction…

A: A detailed solution is given below.

Q: dw I. Find dw and and ду aw (whenever possible) for the following functions. - - dz 1) w = 5x*y –…

A: Let's find.

Q: xVx +1 dx

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Q: 3 By using and only using function composition, show that the following function is its own inverse.…

A: The objective is to use function composition to so that the function is its own inverse.

Q: Use differentials to estimate the relative error in the lateral surface area of a right circular…

A: To find out the relative error in the lateral surface area of the cylinder.

Q: Use Lagrange Multipliers to solve the following: Maximize f(x, y, z) = 4x + 2y + z subject to r? + y…

A: Given

Q: m³ +4m 3. S (1–m*)ž

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Q: sove the focowing using Lagrange Multiptiers: Maximi ze flx, Y, 2) solaject to x2 + y + 22 =1 Ax +…

A: Method of Lagrange Multipliers : 1.) Solve the system of equations .…

Q: Suppose z is a function of x and y, and z^xe^6y=y2+x2. Solve for ∂z/∂x and ∂z/∂y. [b]

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Q: Change the following polar equations to rec 6. 12. r = 4-cose

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Q: Find the vector of length v7 in the direction of AB + AC

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Q: -Sune +1

A: This question is based on solution of Trigonometric equation.

Q: Calculus How many numbers are relatively prime to the following number. - 209 - 323 - 867 - 31…

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Q: Test the series for convergence or divergence using the Alternating Series Test. (-1)^ - 1 5+ 7n n-…

A: Here, the given Alternating series is: ∑n=1∞(-1)n-15+7n

Q: _4. What is the area of the enclosed regions in problem number 3? A. 10 sq. units B. 12 sq. units C.…

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Q: S 3p? tan" p dp

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Q: x2 - 3x -7 dx (x2 + x + 2)(2x - 1)

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Q: 29 – 49 - dy C. 2+ 4y · Evaluate using substitution

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Q: m'+4m (1-m*)7

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Q: 3) lim-) 1 х-1 \x-1 In x)

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Q: The average value of f(x, y) over the rectangle R = {(x,y)| a<x< b, c <y <d} is 1 fave (b – a)(d –…

A: The given expression is: fave=1b-ad-c∫∫Rfx,ydA And fx,y=xy2x2+1 and R=x,y|0≤x≤1, -3≤y≤3 So, a=0,b=1…

Q: Suppose that P dollars in principal is invested for t years at the given interest rates with…

A: Solved below.

Q: e2t (t3 + 5t – 2) - 6+ 5(s – 2)? – 2(s – 2)³ (s – 2)* 6 2 - | (s + 2)* (s – 2)? 8 – 2 Option 2…

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Q: 6. The radius of a sphere is measured to be 7 cm, with a possible error of + (1/10) cm. Estimate the…

A: Volume of sphere   V=3π​r3/4 Percentage error in volume    ΔV​×100/V=3×Δr​×100/r =3*1*100/10*7= 4.3…

Q: 1. Evaluate the integral (22 4т + 4)4/3 da. 3 (a) 1(x+2)1/3 +C 11 (b) (r+2)1/3 + C 3 3 (c) 교 -(x-…

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