3. Find a vector equation of the line that... a) passes through (-3,5,-2) and (7,-3,1)

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bound by…

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Q: A product can be produced at a total cost of C'(x) = 500 + 100x2 + x³ dollars, where x is the number…

A: Given that; Cost function and revenue function.

Q: A rectangular field having an area of 2500m2 is to be enclosed by a fence, and two additional fence…

A: Area=L×W=2500 m2 So,L=2500W The perimeter P=2L+2W+2W {to divide the field into three 2 fences of W…

Q: If z is a function of x and y implicitly defined by əz əz find and əx ду at (x, y, z) = (0, 2, -1).…

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Q: d The series is divergent. . Ignore "Give your reasons" below. There is no need to give reason.…

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Q: Evaluate the y' and Simplify the answers I Direct trigo functions y = x² sinx + 2xcosx - 2sinx

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Q: P N

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Q: 5. Calculate the sum of the first 23 terms of the sequence defined below. tn 10+ 3n, n E N

A: We have to find the sum

Q: B. m(x) = D. h(x) = x+2 x²-4 28. What is the removable discontinuity of x²-4 the function f(x) : = ?…

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Q: Find the area bounded by the parabolas (x - 1)² = 4ay and y² + 4a = 4ax.

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Q: 9. ydx - 4xdy = y'dy; y(4) = 1 Ans: -y²=

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (c) Determine the…

A: Here is the solution of the given problem.  To solve this problem we use simple concept of…

Q: 3. Let 7 and w be vectors such that v=(2, 2, -1), |||| = √2, vw=-3, and × = (2,-1, 2). a. If u =…

A: Key points: We say that 2 vectors are orthogonal if they are perpendicular to each other. If two…

Q: 7. Show that the equation of the plane that has x-intercept a, y-intercept b, and z-intercept c…

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Q: Find the derivative of the following functions. Use long method. a. f(x) = 3x² + 5x - 100 b. f(x) =…

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Q: 2. Determine whether each of the following series converges or diverges. 5n - 2n (2) Σ 3n+4n n=0 +∞o…

A: Given

Q: dy Find the complete solution of 2e2¹ cosx- dx Note: [e"du=e" + C - sin² x = 0.

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Q: x3-4x-10 x²-x-6 dx.

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Q: 0 W³ 6w² +3 dw

A: Given, ∫01w36w4+3dw

Q: 5. We will be able to pay the debts if everybody pays his share. Converse Inverse Contrapositive :

A: To determine the Converse, Inverse and Contrapositive statepements of the following statement.We…

Q: Determine the value of x when the slope is its maximum for the function f(x) = 2cos (3x)

A: Given,  f(x)=2 cos(3x)

Q: line l: x = = and point P(1,0,1). ● Find the set of parametric equations of the line parallel to…

A: Both questions are solved.

Q: A rectangular field having an area of 2500m² is to be enclosed by a fence, and two additional fence…

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Q: 2) Let f be continuous on [a, b], differentiable on (a, b) and positive (i.e., > 0) for all x ≤ (a,…

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Q: Find the slope of the tangent line to the graphof the polar equation 1 TU r = at Ø 1-sino 6

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Q: Evaluate the y' and Simplify the answers I Direct trigo functions y = x² sinx + 2xcosx - 2sinx

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Q: Evaluate the double integral that will find the volume of a solid bounded by z = 4 − x^2 − 4y^2 and…

A: Let's find volume of solid.

Q: Please answer both

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Q: Evaluate the y' and Simplify the answers Inverse trigo functions y = √x² - 4+2arc(csc)

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Q: A product can be produced at a total cost of C(x) = 500 + 100x² + x³ dollars, where x is the number…

A: Solved below.

Q: 1. Solve the differential equation (x-4y-3) dx-(x-6y-5) dy=0

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Q: Find the volume generated by revolving the area bounded by x² - 4x - 4y + 4 = 0 and y = 1 about the…

A: To find the volume generated by revolving the area bounded by x2-4x-4y+4=0, and y=1, about the line…

Q: Consider the vector-valued function R(t) = 1. Find the domain of R. 2. Show that R is continuous at…

A: All three questions are solved.

Q: [₂7-4x dx -2 Determine the value of [4f(x) dx given that [ƒ(x) dx = 10 and ſº ƒ (x) dx = 3. 27 sin…

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Q: Show that the three functions: f₁(x) = ex-8,f₂(x) = ex, f(x) = 4(2x-2) are linearly dependent.

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Q: Find the volume of the solid generated when the region ? bounded by the given curves is revolved…

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Q: -0.45|-2.8x - 4.06| 2.5

A: Here we have -0.45-2.8x-4.06-2.5

Q: ds π Find a particular solution of =10csc² 2t determined by s= 2 when t = - dt

A: Given that the differential equation  ds/dt=10*csc^2(2t) Determine by s=2 when t=pai/4  To find the…

Q: The gradient of the tangent to the curve y=-3x³ + 4ax² - 5x + 4 at x = 1 is 2. The value of a is 2.…

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Q: Determine the Cartesian equation of the tangent line to C1 at the point where 0 = π/2. Given: polar…

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Q: y Let line l: x == and point P(1,0,1). 2 3 ● Find the parametric equations of the line parallel to…

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Q: Solve the differential equation using inspection method d'y d³y = 24. dx5 dx³

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Q: Find the area of the parallelogram with vertices P₁, P2, P3, P4 P₁ = (1,3,3), P₂ = (1,2,2), P3 =…

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Q: Find the Area of the Surface obtained by rotating the curve about the y -axis y = √x, 1 ≤ y ≤2

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Q: 16. Find the area of the region bounded by the given curve: r = 9eº on the interval ≤0 ≤ 2m.

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Q: Determine the x- and y-intercepts for the given function. B(x)=5x+8

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Q: 2.which of the ff.is the reverse process of chain rule?a additional rule b.product rule…

A: Reverse Process of Chain Rule:       The chain rule for derivatives allows to calculate the…

Q: 2x fe²x sinx dx

A: Using integration by part.