dy 1. If (x + y)² = x² + y² prove that 11 I Alx y

Q: 8x²-x+8 x(x² + 4) 2 lnx + 6 in (x²+4)-4 Arctan ¹ (1) + C Option 1 4 Inx+6 In (x²+4)- Arctan (+C…

A: topic -indefinite integral

Q: -2 4.5×10 kg a. T= 2π 2.0×10³ kg/ s b. K = -(6.6×10² kg) (2.11×10¹ m/s)² = 2 -9.0×10 N·m²…

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Q: Determine the angle formed between the following two planes: T1: 5x - 4y+z=3=0 T2: 3x - 4y + 2z+8=0…

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Q: b). Using an appropriate triple integral, evaluate the volume of: [Verify using Mathematica 1). ii).…

A: We have to find the volume.

Q: cos (+h)-cos(3) COS h I {+h)- - 3 3 h 3. Evaluate lim →(7/3) COS 4. Evaluate lim ₁0 π Cos

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Q: Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

A: This question can be solved by the concept of limits and definite integrals.

Q: S dx -1 x-x² 2³√√x 1423 22 Option 1 Option 3 1425 22 Option 2 Option 4 1521 20 1523 20

A: Given: I=∫-8-1x-x22x3dx   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: A rectangular bird sanctuary is being created with one side along a straight riverbank. The…

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Q: A. Find the slope of the line tangent to the given curve at the indicated point. 1. f(x) = 3x + 10…

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Q: The function z(x, y) obeys, = -2e Which of the follow represents a valid first step for finding u(x,…

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Q: 7) Use the double integral of a cross product to find the surface area of x = z² + y that lies…

A: Let's find surface area  by using double integral.

Q: Find an equation of the plane tangent to the following surface at the given point. yz e x² + +42=0;…

A: The given equation is;  yzexz+42=0; (0,-7,6).

Q: In spherical coordinates, the equation below describes what? O a plane O a cone O a sphere O a…

A: topic- spherical coordinate system

Q: Convert the Cartesian coordinate (-1,-4) to polar coordinates, 0≤ 0 0 Enter exact value. 0-

A: Given, (x,y)=(-1,-4)

Q: Find the equation of tangent line to Graph of f(x)=3 x In(5x-4) at point where x=.1

A: Solution:

Q: trahedron enclosed by the coordinate planes and the plane x+2y+z= 8.

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Q: Graph two full periods of the function f(x)=cos(4x) and state the amplitude and period.

A: Given problem:- Graph two full periods of the function f(x)=cos(4x) and state the amplitude and…

Q: 6) F(x, y, z) = (xy²z4, 2x²y+z, y³z²) a) Find curlF. b) Find divĒ.

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Q: I. Solve the following Linear Systems of Equations by Gaussian Elimination: 1.) 6x + 2y4z = 15 -3x -…

A: To solve the system using the gaussian elimination method.

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: Let's find lowest and highest temperature by using langrange multipliers.

Q: B. Find the derivative 11. f(x) = 5x³ 12. f(x)=(x²-3) (2x-3) 13. f(x)=(2²+5)(4x-3) of each of the…

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Q: Let a(t)=20e^-0.3t ( in milligrams) be the amount of drug in a patients body at time t where t is…

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Q: VII. - ) Let C be the curve consisting of the line segment from (0,0) to (2,0), the the portion of…

A: Given that a curve consisting a line segment from (0,0) to (2,0) and a portion of circle from (2,0)…

Q: Find the solution of the following IVP x²y' + 2xy = ln(x), y(1) = 2 1 1 y = ln(x) y=-In(x) - + 3/2 -…

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Q: 6.) I. Simplify. Write "undefined" for expressions that are undefin -3 -6 -2 6 619 1 4 -4 -4

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Q: 1. Find the area bounded by the curve y = x^2  and the x-axis and the ordinates x = 0 and x = 2 2.…

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Q: A driver drove 50 miles in 50 minutes. How many miles per hour was he driving?

A: We have to find how miles cover in 1 hour .

Q: Question 5 Given the function y = f (x) defined at all real values of x. Let x = 2, 3, 5 and 7 are…

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Q: 2 Find the area bounded by the parabola y = 4x and the line y = 2x - 4. 3 sq. units 6 sq. units 9…

A: Given that  :   y2 =4x and y=2x-4 . And we find area bounded by this parabola and line.     Here i…

Q: 3. y= x²-3x-4 x+2

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Q: Find the area of the region bounded by the parabola y² = 2x - 2 and the line y = x - 5. 16 17 18 19…

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Q: Activity #3: Present Value Max was injured and can no longer work. As a result of a lawsuit, he is…

A: We need to find Present value.

Q: Three vectors u, v, and w exist such that - + = 0. Determine the value of ū+uw + (-). w, given that…

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Q: Find the value of the derivative of the function at the given point. 2 f(x) = 3x² − 4x; ( − 1,7) -…

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Q: B. Find the extreme values on the given closed interva 1. f(x) = 4x - 3; [1,5] 2. f(x) = x + 8;…

A: follow next step

Q: (a) Find the general solution of each of the differential equations: dy 8e2x - 4x dy dx = 12e - 10y…

A: Solved below.

Q: 100 (e) Σ199 2i(i3 – 1) i=1

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Q: Evaluate csc(π/6)   Enter the exact answer.

A: Solution ) csc(π/6)  Angle in first quadrant  We know that  Sin x = 1/ csc x  x = π/6 Sin (π/6)  =…

Q: VI. Consider the conservative vector field 1. F(x, y, z) = (z cos(rz) -y sin(ry), 2y cos(ry) - ry²…

A: Solved below.

Q: 4) Use Green's Theorem to evaluate f √1+x³dx + 2xydy. C is the triangle with vertices (0,0), (1,0),…

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Q: Je(ye-1) dr+e dy, where C' is the semicircle through (0, -10), (10,0), and (0, 10). (Compare Problem…

A: Using green theorem, value is evaluated.

Q: Evaluate S ( + - + e²+ =) dz 3 · 3z 21² In x++²x+}x+ + C Option 1 √√(x³)x= √√√x + √2x+C I- Option 2

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Q: I. 2.) Simplify. Write "undefined" for expressions that are undefined. 2 5 3 2 41610 + -6 -6 2 2

A: Given:26-64.53-62+1220We need to simplify.

Q: IVICCE dy Find from the following equations dx Problem (iii) x³ + xy = 0

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Q: Find the general and Singular Solution of the Following differential equation y²Lny = xyP+ P²

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Q: Thank

A: We will solve the problem.

Q: 2) a) Find the unit vectors that are parallel to the tangent line to the curve y = 2sinx at the…

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Q: B. Find the slope of the curve at the given point. 16. 2x²-3x+1 at (2, 3) 17. =3x²-2x+1 at (-1,6)…

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Q: Calculate the area of the segment cut from the curve y = x(3-x) by the line y = x. 2 sq. units 1 and…

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Q: 1. f(x) = 3x + 2, [−2, 2], ƒ (c) = 5 2. f(x) = x² − x + 6,[1,4], ƒ (c) = 10 3. f(x) = 2/2, [-3,-1],…

A: According to the guidelines, we are answering first three subparts. Please repost the remaining.…