(c) Find a function f such that F = Vf where F(x, y, z) = yzi+xzj + (xy + 2z)k.

Q: Find the gradient of the function at the given point. g(x, y) = 11xe/x, (5,0) Vg(5,0) eBook

A: We can find the gradient as below.

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A: Given,  y=xex9, 0≤x≤5

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Q: a b = A = B Note: Triangle may not be drawn to scale. Suppose a = 6 and c = 7. Find: B = b O A O

A: Solution: Given:  a=6,    and c = 7 Using Pythagorean theorem

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Q: Write an expression for the polynomial of least possible degree graphed below. Leave your answ…

A: The solution is given below

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Q: M8 K-0 3 900+3k

A: Given, ∑k=0∞3900+3k

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A: We have to find solutions

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Q: What is the original price of P1,743,759 discounted price at 22% discount?  (whole number)

A: discounted price = 1,743,759  discount rate = 22%  find original price = ?  this discounted price is…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: Sketch the region of integration and change the order of integration f x I 1 = [²] [~ ² f(x, y) dy…

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Q: 5. 6. Sexcos2x dx |— S- dx 3 (x + 2)² − (x+2) ² -

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Q: 1) Solve the following ODES by Undetermined Coeff. ● 4X 11 X y - 16 y = 19.2 € + 60e, y(a) = y() -4X…

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Q: at ch Use the Fundamental Theorem to show that the following is true. a f b C b [ f(x) dx = ff(x)dx…

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Q: go Find the equations of the tangent lines to the graph of y=x²+6 graph of a to 197 +6 that through…

A: To find out the equation of tangent line and also graph it.

Q: Evaluate lim 74 x →0 COS 218

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Q: A local club is arranging a charter flight to Hawaii. The cost of the trip is $543 each for 83…

A: We need to find no. of passengers and max. revenue.

Q: Evaluate the following integral and express in exact form: cos(x/2) sin(x/2) dx

A: SOLUTION-

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Q: Find the solution of the given initial value problem: y (4) + 2y"+y = 3t+6; y(0) = y'(0) = 0, y" (0)…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. x+y+z= 12, (4, 3, 5)…

A: Our Aim is to find :-(a) An equation of the tangent plane to the surface at the given point.Here…

Q: 1. Find the area of the region bounded by the curves y=sin X16 , y = 0, and x = 6 obtained by…

A: topic - Area bounded by curves

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Q: Find the critical numbers for h(x)=x^2-x^4. Show all work.

A: The objective of the question is determine all the critical point of the given function.

Q: 1 g(x)= {x-1 if x > 0 |x² −1 if x≤0

A: The given function, gx=1x-1if x>0x2-1if x≤0

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Q: Find the distance from the point A to the line through points B and C. Then show that the triangle…

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Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = P(2, 3, 4),…

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Q: 1. Evaluate the double integral r²y dA, where D is the region enclosed by the x-axis and the…

A: We can evaluate the double integral.

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

A: here is the solution:

Q: Perform the matrix operation( multiplication of 3x3) 1 3 2 1 4 -3 02 3 LO 0 -4 [0 3 0 0 2 -1] 2

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Q: Find the inverse function and graph both f(x) and f(x) on the same set of axes. Check your work by…

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Q: Solve the initial value problem: y(x) = 2x - 4y√x² + 1. dy dx = 0, y(0) = -4

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Q: The father has just donated $25,000 to a church. His son would like to donate an equivalent amount,…

A: Given;  Principal =$ 25000 Time = 5 years  Rate = 8.2%.

Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

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Q: how long will it take for the money in an account that us compounded at 8% interest to quadruple

A: