Find div F if F(x, y, z) = (x² + y)i + z²j + (eY - z) k.

Q: dyx+2y 2x+y dx

A: We have to find the general solution of differential equation

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Q: Evaluate if possible 1 [₁²x5+¹ dx -2 x3 ….…..

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Q: Sketch the space curve. Vector-Valued Function r(t) = −ti + 3tj + 4tk Interval [0, 1]

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Q: Given: f(t) = 8 sin23t. Evaluate: F(1) Use 2 decimal places.

A: f(t) = 8 sin23t.

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Q: Find the curvature K of the curve, where s is the arc length parameter. r(s) = (2+ s)i - j K= eBook

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Q: Find curl(2z + 3x j + 6y k). curl(2z i+ 3xj+ 6y k) = (i )i + (i )j + ( i )k

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Q: Find the following values. Round answers to 3 decimal places as needed. csc(-13°)~ sec(5)≈ tan( -8)…

A: Basic trigonometric transformations are required

Q: ² x (√x + √x) dx

A: We know that integration power rule is  Integration of xn is xn+1/n+1 + C. Here C is integration

Q: If f(x, y, z) = 1, then fff f(x, y, z)dV gives the volume of V.

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Q: Find r(t). u(t). r(t) = (3t − 4)i + ¹1t³j + 4k 4 u(t)= t²i - 8j + t³k r(t). u(t)= Is the result a…

A: To find: rt·ut Given information: rt=3t-4i+14t3j+4k ut=t2i-8j+t3k

Q: Find the derivative of the function. f(x) = arcsec(4x) 1 xV 16x²-1 x

A: Topic = Derivative

Q: Determine the interval(s) on which the vector-valued function is continuous. (Enter your answer…

A: Given problem:- rt=13t+1i+1tj Determine interval(s) on which given vector valued function continuous…

Q: Use the formula k(t) k(t) = "(t) || ||r' (t)||³ r(t) = 11 cos(3t)i + 11 sin(3t)j + 2tk ||r' (t) = to…

A: The given formula is; κt=r't×r''tr't3 And rt=11cos3ti+11sin3tj+2tk   As we know the Chain rule:…

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: Find the critical point of the function. Then use the second derivative test to classify the nature…

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Q: fy X = = 11 f(x, y) = (x² + y2)2/3

A: Given the query is to find indicated partial derivative.

Q: Use Green's Theorem to evaluate the line integral Ico (y - x)dx + (2x - y)dy for the given path. 3π…

A: Solution is given below:

Q: 3. 2-y x-2y

A: Give the general solution of the following Differential equation.      dydx=2x-yx-2y

Q: 4. Use the special properties of logarithms to solve the following equations. a. M = log₁11²1 b.…

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A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

A: The Domain of the function is the set of all possible input values for which function is defined.

Q: Find the general solution of the given differential equation. dy 2 +6y=3 dx x(x) = 2 Give the…

A: To find the general solution of the given differential equation.2dydx+6y=3To give the largest…

Q: 4. Consider the function f(x) = 3, a) Evaluate lim ƒ(x) and lim_ f(x). x-0+ x-0- c) Is f(x)…

A: Let's solve limit problem.

Q: Suppose that f(x,y,z)=(x,y,z)=2x+4y+3z at which x^2+y^2+z^2≤3^2 Absolute minimum of…

A: Please see the below picture for detailed solution.

Q: solving

A: Please refer to the image below

Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

A: The given function is: fx=x4-5x3   As we know that; If f''x>0, then we get the interval where the…

Q: A manufacturer can produce 4860 cell phones when a dollars is spent on labor and y dollars is spent…

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

Q: 4). Use the Integral Test to determine whether the sum converges. ∞     n = 1 n 1 + n2

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Q: Sketch the plane curve. r(t) = 3ti - tj, [0, 3] O y 3 2 1 -1 -26 " 3₂ 3 2 1 -1 -2 2 4 4 Find its…

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Q: 1 For r(t) = − i − j + m(1) k - j + ln(t)k and u(t) = t²i − 2tj + k. t d Find [r(1) · u(1)] ²3 +…

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Q: Solve the equation on the interval 0 ≤0<2 cos (30)=1 MAN What are the solutions to cos (30) = 1 in…

A: Solve the trigonometry equation

Q: and the first partial derivatives of the function. f(x, y) = 4y

A: Given the query is to find indicated partial derivative.

Q: Find Vy where = (x² + y² + z²) e¯¯ √√√x² + y² + z ²

A: Given :ψ=x2+y2+z2e-x2+y2+z2

Q: units

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Q: NOTE: Enter the exact answer. 13 [ ²³ | = [ |ti + t²j|| dt

A: Given: ∫013ti+t2jdt

Q: Find curl(5zi + 6xj + 3yk).

A: Our Aim is to find the curl 5z i^+6x j^ +3y k^-(i)

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Q: DETAILS ZILLDIFFEQMODAP11 4.1.002. The given family of functions is the general solution of the…

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Q: Question Number 4: [CLO2, PLO1] Determine the concavity of the parabola representing the quadratic…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for you. If…

Q: 4. Which of the following is the vector projection of (1,0, 1) onto (-2, 4, 0)? 2 B. (-1,2,0) c.…

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Q: Find the absolute maximum and minimum of f(x,y)=4x+3y within the domain x^2+y^2≤16 Please show your…

A: Concept: Absolute maxima of a function refers to its highest point within its whole domain, whereas…

Q: Find ▼ · (V × F) if F(x, y, z) = 8 sin xi + 8 cos(8x − 9y)j + 10zk. V · (V × F) = [

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Q: 1. (ex-y)(1-e²y)¹/² dx = dy

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Q: Evaluate the definite integral. [²³ sin5(x) dx Step 1 6.² sin5(x) dx, first rewrite the integral. To…

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Q: Find dy/dx without changing the form of the given function and answer must be in the simplest form:…

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Q: Let m(x) = etanx). Which of the following best describes its fundamental algebraic structure? A. A…

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Q: Determine the vector field of F. F(x, y) = 4i - 2j O O Y X X

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