1. Which of the following relations is a function? a) {(1,9), (2, 4), (2, 3), (4, 15)} {(2, 7), (7, 9), (9, 7), (3, 14)} c) {(5, 1), (7, 1), (5, 6), (12, 1)} {(1,4), (1, 12), (8, 13), (16, 23)} b) d)

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A: I am attaching image so that you understand each and every step.

Q: Q4. Find the values of the constants a, b, c so that - F = (axy + bz³)ī+ (3x² − cz)j + (3xz² − y)k…

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Q: Find the limit. x²y lim (x,y) → (0,0) x² + 8y²

A: limx, y→0, 0x2yx2+8y2

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A: Topic -Definite integral In definite integral, Area below x-axis is considered as negative.

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A: The objective of the question is evaluate the differential equation.

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A: Topic - indefinite integral ∫xndx=xn+1n+1+C

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A: Solution is given below:

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A: Given :   xdx+sin2yxydx-xdy=0

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A: Please see the below picture for detailed solution.

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Q: i) lim cos x-0 7 πCOS²x x²

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Q: xy - Y lim(x,y)→(1,0) (x − 1)² + y²

A: Please see the below picture for detailed solution.

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Q: 5. Let f(x,y) = x² + xy + y² be a function on the domain D = {(x,y) = R²: x¹ + y ≤ 8 and y ≥ 9}. a)…

A: Given fx, y=x2+xy+y2 Domain D=x, y∈R2; x4+y4≤8 and y≥9

Q: Let à = = (2, 4, 5) and 6 = (3, -5, - 2). - Find the angle between the vector (in radians) Check…

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Q: When completing the square for the quadratic equation shown below, how is c calculated?

A: Our Aim is to show how c is calculated when completing the square for thequadratic equation…

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Q: Compute the given integral. fcos¹ a a sin ædx = +C

A: Our Aim is to evaluate the integral given below:-∫cos7 (x) sin (x) dx -(i)

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Q: Differentiate the following function. You do not need to simplify the derivative. dy dx || y = 2e²²

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Q: Differentiate the following function. You do not need to simplify the derivative. F'(x) = F(x) = 6e²

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Q: Q-3: a) b). Using logarithmic differentiation, find the derivative of -3x√2x-5 (6-5x)4 - 34x = 0.…

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Q: Solve (2y³ – x³) dx + 3xy² dy=0; y (1) = 1 O a. x² (5y³ x ³) = 4 b. ? (5y® — g - 23) x³) = 0 ○ c. x²…

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Q: If C(x) = n=0 ∞ n=0 2n + 1 2n + 2 2n ²n and S(x) = ∞2n+2 2n + 3 n=0 -x²n+ find the power series of…

A: The given power series, Cx=∑n=0∞2n+12n+2x2n and Sx=∑n=0∞2n+22n+3x2n+1

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Q: Use reference angles to evaluate sec (11"). 3 Enter the exact answers. For the number 7, either…

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Q: se the limit definition to find the instantaneous rate of change of f(x) = 3x^2 - 4x at x= -3.

A: The instanteneous rate of change of a function f(x) at x=a is the limit of the average rate of…

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Q: Let r(t) = (-5t¹-2, - 5e³t, 2 sin(3t)) Find the unit tangent vector T (t) at the point t = 0. Round…

A: This question is related to differentiation, We will solve it using given information.

Q: Match each equation in rectangular coordinates with its equation in polar coordinates. x² + y² = =…

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Q: Find the curvature of the curve r(t) = (5 + 4t, 4 - 4t, 1 - 3t) at the point t = -6. Check Answer

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