5. Evaluate lim x→2 x² - 16 X x-2

Q: Calculate the divergence of the vector field F=x²y³z¹i-xyzj+(x+y+z) k

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Q: What is the solution of the given ODE * xy' + y = √x /2 x = {√x + ² y = {√x + = 2 y 1 x Option 1…

A: Given problem:- What is the solution of the given ODE*   xy' +y= √x

Q: Properties Of The Dot Product (- 2-.. pesta ) n. v = 0 = i = 0 or D = 0or ii 1 v تريلية

A: We have to prove the given property.

Q: 1. For the vectors v = and u = a. Find vou b. Find ||v|| and ||u|| c. Find the angle between v and…

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Q: 5. [7.6] If vectors ū=(5,2,-1) and = (2,-1, 3) then... a) determine u x v. b) Explain the geometric…

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Q: The surface parametrized by 7(u, v) = (u, v, u - 2v) is a plane O a hyperboloid a cone a cylinder

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Q: Question 10 The function y= ax6x³ has a minimum point at (2a, f(2a)). Determine the value of a. - a…

A: Let's find a value.

Q: Ice O 3.19 O 13.9 O 12.6 O 16.1 O none of the above (ezt - e-²t)² dt

A: Given that a integration and we solve this integration by using general formula of integration. Here…

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: Now find the area bounded by y= x^3, x=0, and y=3 a) 3.25 b) 3.28 c) 3.26 d) 3.27 integral…

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Q: Find the area of the region bounded by y = x³ - 8 the x-axis and the y axis. 1/3 3 1/9 9

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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: The rate of a continuous money flow starts at $600 and increases exponentially at 2% per year for 15…

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Q: 1.) a function f f (x,y, 2) = 2-eªsing is given. of this function p= ((n 3, 31,-3) at the point what…

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Q: The ellipse + 1 can be drawn with parametric equations where (t) is written in the form 4²2 r(t) = r…

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Q: Convert the rectangular coordinates (5,-5√3) to polar form. Letr> 0and 0 <0<2TT.

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Q: Use a double integral to find the volume of the solid region under the paraboloid z = x² + y² and…

A: Use double integral concept

Q: Question 18 If F is a conservative vector field in R³ and C is a loop (curve whose initial and…

A: To find which thing is true about given line integral.

Q: 10 What is the 6th term of (x − 1)¹⁰-

A: Please refer to the image below

Q: Determine the interval(s) where f(x)-In (5x+10) is continuous. It is continuous in the interval

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Q: 1. Find the Inverse Laplace Transforms of the following. 4) 48-60√/s s4

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Q: What is the 6th term of (x - 1)¹0?

A: Given problem:- what is the 6th term of (x-1)10

Q: Find the linearization of the function f (x) 1 9x+8 at = -1. L(x) = -9x-10 si Find the true values…

A: This question can be solved using the concept of linearization of function.

Q: Test for convergence/divergence, State the theorems used.

A: As per guidelines, I can answer only one question. Since questions are not interlink with each…

Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

A: Given ∫(sinx)3dx=∫sin3xdx

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: ||. Minor and Cofactor 1. Find the cofactor of 6 in matrix D 9 8 4 2 7 -9 3 4 D = 6 -3 2 3 8 9 3 2 ㅋ

A: Let's find cofactor of 6 in matrix D.

Q: Integrate. Simc 1 In (6x) dx

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Q: n Express the function n, lim 21³ n→+∞ n5 i=1 and then find the limit. in closed form

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Q: a 1. The graph of y = where a is a constant is called the witch of Agnessi (named after 2 x²+a² the…

A: To find the derivative and equation of line tangent to the given curve.

Q: In cylindrical coordinates, the equation below describes what? O a vertical plane O a horizontal…

A: Given :   r=5

Q: 26. *2# 70 x² sin x dx

A:

Q: Find the area contained between the two curves y = 3x - x² and y = x + x². 1/3 sq. units 1/4 sq.…

A: Let's find area between two given curves.

Q: Use the parametric equations of an ellipse, x = 5 cos (0), y = 4 sin(0), 0≤ 0 ≤ 2π, to find the area…

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Q: (EQUATION

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Q: Find the Cartesian equation of the plane containing the point P(1,3,-2) and the I T = (0, -1, 4) +…

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Q: Calculate the gradient of f(x, y) = sin(x² - y) Vf=

A: Finding the partial derivative of the function.

Q: Option 3 + 7 2x2 7 ALL OF THE ABOVE

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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: Let R be the region in the first quadrant bounded by x^2 +y^2 =4, y^2 = -x+4 and y=0. Set up the…

A: We have to find the area of the given region.

Q: Evaluate S√9-4x² dx a. 0.285 b. 0.123 c. 0.423 d. 0.365 e. NONE OF THE ABOVE

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Q: n=1 n 2n+1 2n-1 xch

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Q: Suppose z = f (x, y), where x (s, t) = 2st and y (s, t) = s t + 7. af af At point P, suppose = 3 and…

A: Here we have to find a partial derivative at a point.

Q: Let x = [X₁ X2 X3]. Find the matrix A such that the system x' (t) = Ax(t) + f(t) is equivalent to…

A: Here is the solution of the given problem. Differential equation to system of differential equation.

Q: What is the exact value of sin(255°) +sin(195°)?

A: find value of  sin(255) +sin(195) here this is trigonometric function  lets find value of this

Q: Evaluate the double integral: So Son VV (Hint: Change the order of integration to dy dx.) sin(7³) dr…

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Q: A gas station sells Q gallons of gasoline per year, which is delivered N times per year in equal…

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

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