6 Find the local Minimum and Maximom Values and Saddle 1 + (x₁92 = 22²¹ +p² +8x-6p 120 points

Q: Use Stokes' Theorem to evaluate 6 F. dr where C is oriented counterclockwise as viewed from above.…

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Q: Evaluate the integral. Check your answer by differentiating. (Remember the constant of integration.)…

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Q: Replace the Cartesian equation x-y-19 with an equivalent polar equation. The equivalent polar…

A: Given the cartesian equation is x-y = 19. We have to convert it into an equivalent polar equation.

Q: In 1932, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase.…

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Q: Lyds, yds, C: x = t², y=t, - 2 ≤ t ≤ 8 Evaluate Calculator Check Answer D

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Q: Find the solution r(t) of the differential equation with the given initial condition: r(t) = ( r'…

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Q: Starting from the point (−4, −2, −4) reparametrize the curve in terms of arclength. r (t (s)) = i+ r…

A: Arc length.

Q: Use the Divergence Theorem to calculate the surface integral F(x, y, z) = (x3 + y³)i + · (y³ + z³)j…

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Q: Consider the following. Function f(x) = 6 cos 2x (a) Use a graphing (x, y) = ( (x, y) = ( (x, y) = (…

A: Consider the following. Function: fx=6 cos2x Trigonometric Equation: -12 sin2x=0 (a) By using a…

Q: The area of the surface generated by rotating the curve y = 1 -e ¹, where -3 ≤ x ≤ 3, about the…

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Q: = The region D above lies between the two red lines and the red parabola y describe in two ways. 4…

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Q: Evaluate the integral. Check your answer by differentiating. (Remember the constant of integration.)…

A: The integral is ∫34+x10dx

Q: For the given cost function C(z) = 62500 + 300x + z²

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Q: Find all values of x for which the following is true. (Enter your answers as a comma-separated…

A: We need to find the values of x for which the determinant of the matrix is 0. The matrix is:…

Q: Find the limit. Use l'Hospital's Rule if appropriate. Use INF to represent positive infinity, NINF…

A: We are required to find:limx→02ex-2-2x9x2

Q: Consider the vector field F = • /. F F. dr along the curve C: F(t) = 3 cos(t)i +3 sin(t)], 0≤t≤ 1…

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Q: Question 1 Let R be the region bounded by y=x, y=2x, x=1, x=2, and I= SS. - dA. 6 y x² + y² 2 a)…

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Q: Convert the angle 315° to radians. Give the exact valu and use pi for π.

A: Given angle θ=315°

Q: 3.Describe the largest set S on which it is correct to say that f is continuo a. f(x,y) =· x² + xy-5…

A: Given function is f(x,y) = x2+xy-5x2+y2+1 we have to find the largest set S on which f is…

Q: If r(t) = = cos(-3t)i + sin(−3t)j – 10tk compute r' (t)= i+ i+ (cos (-3t))/3 and fr(t) dt= (-sin…

A: r(t)=cos(-3t) i+sin(-3t) k-10tk

Q: Without using a calculator, compute the sine and cosine of 300° by using the reference angle. What…

A: Reference angle for the angle t in the fourth quadrant is: 360-t

Q: 9.3 Find the directional destive of f(x,y) x²x4²x4² at (1,1) in the direction of √(3,4)

A: Find the directional derivative of f(x, y)= x3 y4 + x4 y3 at (1, 1) in the direction of v(3, 4).

Q: nd an equation for the line tangent to the curve at the point defined by the Py at this point.…

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Q: Solve indefinite integral with steps: sin5x*cos((2x)/5)

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Q: The sum of the perimeters of an equalateral triangle and a square is 10. Find the dimensions of the…

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Q: Definite integrals: 10 S," = 1 -dx x²-4 3 S* (2sin(x) - ex) dx 0 Indefinite integrals:

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Q: Find xy² Una -dA, R= [0,4] × [-2, 2] x² + 1

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Q: Suppose that f(x, y) = 4, and D = {(x, y) | x² + y² ≤ 16}. Then the double integral of f(x, y) over…

A: f(x,y)= 4.  The graph of domain is

Q: A 5.00-ft-tall man walks at 8.00 ft/s toward a street light that is 17.0 ft above the ground. At…

A: Given data is as follows  A 5 ft tall man walks at 8 ft/s towards the street light that is 17 above…

Q: 1. Let f(x,y)=x²y + √y Find each value a.f(2,1).b.f(3,0).c.f(1,4)

A: We have to find the value of the function for the given points, f(x,y) = x2y + y points : f(2,1)…

Q: If f '(x) = 8x7, what is f(x)? (Remember the constant of integration.) f(x) =

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Q: Find the length of the curve. 3/2 x=y= (2t+1) Osts 12 The length of the curve is 220. (Simplify your…

A: Curve length.

Q: -1 Evaluate the expression cos sin Give your answer as an exact value 2π 3

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Q: Put the steps for solving an applied optimization problem in the correct order. Take the derivative…

A: To optimize maxima/minima problem use use derivative test as follow:

Q: 1.Find the indicated limit or state that is does not exist lim(3x²y — xy³) a. b. (x,y) →(1,3) lim…

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Q: Let r(t): = 1 t-1' +-1/2). Find the domain of r(t). et+1, t-1,

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Q: Suppose (t) = cos(πt)i + sin(πt)j + 3tk represents the position of a particle on a helix, where z is…

A: The height of the particle is calculated by the z component.So,we get the time when the particle at…

Q: Iodine-125 decays at a regular and consistent exponential rate. The half-life of Iodine-125 is…

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Q: Find the length of the curve. x=8t², y=121²,0sts √8 The length of the curve x=8t", y=12t² on 0sts √8…

A: Given curve x=8t3,   y=12t2    0≤t≤8

Q: 4 B C D 1 3 t ST 3 7 T 4

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Q: Find the absolute maximum and minimum of f(x, y) = 1x + 2y within the domain x² + y² ≤ 5 1. Absolute…

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Q: Find the surface area of the part of the plane z = 5 + 6x + 3y that lies inside the cylinde x² + y²…

A: Area=∬D1+∂z∂x2+∂z∂y2

Q: et F(x, y) = 5xy21+ (5yx² + 5y)j, and let C₁ be the curve consisting of the circle of radius:…

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Q: a) Find the exact length L of the curve 1 y = = = (x² + 2) ² ₁ 0 ≤ x ≤ 3, 3 b) Can you say, without…

A: a) Find the exact length of the curve  y= 13x2+232, 0≤x≤3 b) Can we say, without calculating, that…

Q: Solve the system of equations using Cramer's Rule if it is applicable. 8x = 32 2x + 4y = 0 ww. Write…

A: We need to solve the given system using Cramer's Rule: 8x=322x+4y=0

Q: what value of a will make instantaneous rate of change for the function y = 3x2-x-2 whe f(x) =

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Q: Evaluate the integral. Check your answer by differentiating. (Remember the constant of integration.)…

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Q: Use your answer above (and more differentiation/integration) to now express the following function…

A: g(x) = 1/ (7+x)3

Q: Apply L'Hôpital's Rule to evaluate the following limit. It may be necessary to apply it more than…

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Q: A box with a square base and open top must have a volume of 62500 cm³. We wish to find the…

A: We know that volume of the box is the product of area of the base and the height of the box.  Let x…