The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of the normal line through this point is L(t) =

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A: To use green's theorem to find the given line integral over the curve C

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A: Study of integrals in calculus is motivated by calculating the area of a region bounded by curves.

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A: LetI=∫sinθcos2θ+cosθ-2dθPut cosθ=uDifferentiate on both…

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

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A: To verify green's theorem by evaluating both the integrals.

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Q: b) Use L'Hôpital's Rule to evaluate the limit L. e2x lim X→∞ x2

A: We can solve part in the following steps.

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Q: 2r-4-x 2-2r 3 in Ir+1+3Inlx-3|+C +1-3hx-31 +C Option 1 Option 2 2 In Ix + 1-31nlx-31+ C 2 In Ix+ 1+3…

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Q: x² + 4x + 1 dx (x – 1)(x + 1)(x + 3) d* - Inlx- 1+Inlx+11- n|r+ 3| +C Inlx- 11+Inlx+1| +Inx + 31 +C…

A: Let's find.

Q: Find the global minimum of the function f(x)=2x^3+3x^2–12x+4 on the interval [-4,2].

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Q: Use the first fundamental theorem of calculus to find F'(x) F(x) = [ cosr' dt

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Q: 1 19 9. -10 -k Consider the matrix it corresponds to an augmented matrixial representation of a…

A: To find for given conditions of alpha and k and the system have how many solutions.

Q: Find the divergence of the vector field F. F(x, Y, z) = In( 9x²+ 8y² )i + 72xyj + In(8y² + 7z? )«…

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Q: Suppose the revenue function for a product is given by the function: : R(g) = - 8g° + 4g where q is…

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Q: The marginal cost for a company to produce q items is given by MC(q) = 0.004q - 0.9q + 615. The…

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Q: :. Let x(t) = 2 sinh t , y(t) = cosh(t²) be a curve in the Oxy-plane, given in parametric form. (a)…

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Q: Which of the following is an antiderivative of f(x) = sin x cos x? %3D (a) sin²x (b) cos² ¤ sin 2x…

A: We can find the answer as below.

Q: Find all the critical points of the function f(x, y) = x³ + y³ – 9x2 – 21x – y - 66 and label them…

A: Local Extremum values:              Consider the function f(x,y) .For critical points , fx(x,y)=0…

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A: Trigonometric values cot2π6=32=3 sec2π4=22=2

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Q: Consider the parametric equations below. Assume that t can be any real number. x=t-3, y=2t-5…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 2° , y = 0, and z = 5,…

A: We have to find the volume of the solid.