Q3- Sketch the region of integration and evaluate the integral: In8 Iny ["C ex+y dxdy

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 9(x² -…

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Q: The acceleration of an object (in m/s²) is given by the function a(t) = 8 sin(t). The initial…

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Q: Water is poured at a rate of 10 cubic meters per minute into a conical tank 6 meters across the top…

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Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² =…

A: Let's find surface area rotated about x=0.

Q: Complete the parametric equations for the line where the planes - 7x + y + 3x = 3 and 4x7y + z = 23…

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Q: Evaluate the given integral by changing to polar coordinates. 4x²y dA, where D is the top half of…

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Q: In the diagram, AABC is an equilateral triangle, and D, E and F are the midpoints of its sides.

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Q: Integral Calculus

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Q: Evaluate 1₁ 2 t(1 + Int)² dt

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Q: 3 Find the arclength of the curve y = (x² - 4) on [2,4].

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Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 2(x² -…

A: Above question is solved.

Q: Find an equation for the line tangent to the graph of y = tan ¹ (2x) 2 1 What is the tangent line to…

A: As we know that; The slope of the tangent line to the given curve is equal to the first derivative…

Q: expand using the binomial theorem. simplify (a+b)^2 (2x^2 -1/x^2)^4

A: solution

Q: Q4: Evaluate the following integral. 7/21/2 sin y 5% dy dx Y

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Q: Describe the type of discontinuity at x = -1, explain your answer. Use the definition of continuity…

A: a. Type of Discontinuity: Removable Discontinuity

Q: Find the cross product a x b. a = (4, 5, 0), b = (1, 0, 9) Verify that it is orthogonal to both a…

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Q: nverse for the following functions. If it does not exist, show why. f(x)=2x-1 f(x)=√x-3 f(x) = |x-1|…

A: Topic:- calculus

Q: Given that f(x) = (x - 2)² and g(x) = 1 - 3x, find (a) (f + g)(4)= (b) (f - g)(4)= (c) (fg)(4)= (d)…

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Q: The height of a certain amusement park ride follows the function h(t) = −³+ 11t² — 32t + 28, where…

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Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

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Q: 12. etan 2x sec² 2x dx 13. Jdx/(x²-4) 14. (2x¹-x²) dx / (2x² + 1) 15. f (sec²x) dx/(√(1-4 tan² x))…

A: Given

Q: 5 ;ㅣ

A: We have to find first four terms of give series.

Q: integral

A: We will find the solution m

Q: BIN 2 sin² x cos x dx

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Q: Find the point at which the line x(t) y(t) z(t) - 5+ 5t -6-8t intersects the z plane. - 7+8t

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Q: Find a scalar equation of the plane x + 2y + 3z = 0 -x+ 3y - 2z = 0 c. 13x + y - 5z = 9 d. 13x+y- 5z…

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Q: 5) An isotope of lead decays according to the function remaining, in grams, after t minutes. a) What…

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Q: 4. A 25-ft long ladder is leaning against a vertical wall. The foot of the ladder is on a horizontal…

A: Note : According to our guideline I can solve only 1st , please reroute the remaining question.

Q: 4. The equation of a plane is [x, y, z)=[-1,-1,1]+s[1, 0, 1]+[0, 1, 2]. Find the - intercept of the…

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Q: lim 818 sin n+1 n + sin n+2 n + sin n n+3 n +... + sin (2) = cos(1) - cos(2).

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Q: Find the volume of the given solid. Under the surface z = 1 + x²y2 and above the region enclosed by…

A: To find the volume of the given solid.

Q: a. g(3) = = b. lim g(z) C. lim g(z) d. lim g(z) = Z-1 = -4 -3 -2 -1 10 6 2 0 -2 -4 -6 9(z) 2 3 5 6

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Q: Let a, be such that asb. Prove that tx Eqt ax cbx

A: Concept: We have a,b∈Q means that a, and b belongs to the rational numbers and a<b means that a…

Q: 5.1 Let a eR, v = 4ai - 6j and w=a²i +3j. Determine all nonzero values a, if any, so that is…

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Q: √√-x-6 if x < -1 Let g(x)=2x-3 if-1<x<4 6-e-4 if x ≥ 4 a) Give the domain of the function. b) Is…

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Q: d=(-3,-2) and 6=(2,4). Represent a-6 using the head-to-tail method. Use the Vector tool to draw the…

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Q: (x²+2) dx x+2

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Q: Q3) Given, u (x, y) = xy is harmonic, find a harmonic conjugate v(x, y), write u+iv as a function of…

A: As we know that for complex analysis z=u+iv   then u and v are conjugate to each other.Then by…

Q: Use the transformation to graph the given function. Show all of the transformations on the same…

A: We have to translate the graph

Q: x³-y³ Determine whether the function z = g(x, y) = x² + y² (why or why not) for for (x, y) = (0,0)…

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Q: A manufacturer has modeled its yearly production function P (the monetary value of its entire…

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Q: A stone is released with zero velocity from the top of a tower, reaches the ground in 4 sec. The…

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Q: Given an acceleration function a(t)=, find velocity and position functions, given that v(0)= and…

A: We have to find solutions

Q: (a) Find where x² + 3xy + y² = 3 at (√3,0). da

A: topic- implicit differentiation

Q: Which of the following vectors is coplanar to [1, 1, 1] and [1, 2, 3]? O a) [4, 2, -2] b) [5, 7, 6]…

A: Given vectors  [1,1,1] and [1,2,3] For coplanar with another vector, the determinant should be zero.…

Q: How firel the center, foci, vertices and eccentricity for the following equations! x+4y²-4x-8y +4=0…

A: Concept: Ellipse: The equation of the ellipse with center at (h,k)  (x-h)2a2+ (y-k)2b2 =1 Hyperbola:…

Q: Evaluate the iterated integral. "TU 2 √4-22 ²² z sin(x) dy dz dx

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Q: h pendant. In one setting, the two diamonds would have a mas e second setting, the mass of two…

A: Topic:- algebra

Q: f(x csc² 2x - x cos 2x)dx

A: Here we to integrate the given integral

Q: If dx = e-²y and y = 0 when x = 5, then the value of x when y = 3 is dx e6 +9 A. e5 C. 2 B. e6 + 1…

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