Find the shortest distance r1 between the two lines given by r₁ (t) = (3 + t, 3t, 5 – 4t) and r₂ (t) = (–t, t, 2t).

Q: For the following exercise, find the volume generated when the region between the curves is rotated…

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

Q: x²+1 lim x-5 √2x+2-2

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Q: Evaluate the integral. 7 7 √49-x² ILL 1 /49-x² (x² + y²)1/2 dy dx dz =

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Q: 7. Find the equation of a normal to y = x³ - 3x²+x-1 at x = 3

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Q: sec¹ (3x) b) ›1$ 3 tan³ (3x) dx

A: I have stated the used formulas in the solution

Q: Problem 1. You are fencing in an area next to your house so your cats can lounge outside. The cat…

A: We have given the length of material that is avialble for fencing is 27 feet.

Q: √√√x- S: z 12, x² + y² ≤ 1 Evaluate (x - 2y + z) ds.

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Q: 1. Factor the following completely. a) 16x² - 100 b) 15x²-3x - 12

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Q: 5) each k=1 (- series, find the sum. k - 1 6) k=1 +1) (k+2)

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

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Q: 8. Evaluate F. dr using Stoke's theorem when F = (2xy — x²)ī — x² − y² )ī and C is the boundary of…

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Q: question: 2. xdy + (xy - y - y²) dx = 0 answer: 2.y = x Cex+1

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Q: Consider the vector whose initial point is P(-6, 1) and terminal point is Q(-5, -3). Find the…

A: We need to find vector.

Q: Let the position function of a particle be r = <t, t2,0〉. Find the tangential component of the…

A: Let the position function of a particle be r=t, t2, 0.To find the tangential component of the…

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Q: Let r(t) = (-5t5 - 3, 4e-4t, 5 sin(2t)) - Find the unit tangent vector T (t) at the point t = 0.…

A: Given vector  r(t)→=&lt;-5t5-3,4e-4t,-5sin(2t)&gt;

Q: Evaluate the integral: Fa ○ x = 6 sin(0) ○ x = 36 tan(0) 28 x²√x² + 36 dx (A) Which trig…

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Q: Given x = y² +y + 1 from 0≤y=2 The Arc Length of the given curve over the interval is a. 7.38 units…

A: I have stated the used formula in the solution

Q: (a) Find an affine change of coordinates that takes the unit square with vertices in the uv-plane to…

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Q: 7. Find: y = In dx √6x-5 [ Lex (x+1)³.

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Q: EX #3: Roller Coaster A hypercoaster is a special circuit roller coaster with a height measuring…

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Q: Let f(x) = ln(x² + 2x + 6) f'(x) =

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Q: Let f(x, y) = 2e sin(4) of д х of dy Check Answer

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Q: Find the cross product u x 7 where u = 51 -3j+k and = (-1, -3,2). uxv=

A: To find the cross product u→×v→ where u→=5i-3j+k and v→=-1, -3, 2.

Q: Differentiate the following function. You do not need to simplify the derivative. f(x) = (In x)5…

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = ln(x + 5y + 6z). F(x, y, z) = =

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Q: Use the graph of ƒ (x) = x² below to find a number & such that x² − 1| < 0.5 whenever 0 < |ï − 1| <…

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Q: 4. 5⁰ -x² xe dx

A: Given Problem:- ∫0∞xe-x2dx

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Q: = Using calculus, find the absolute maximum and absolute minimum of the function f (x) [-3,2].…

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Q: ㅠ 10. fž sint p cos3 p dp 2

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Q: 5. (y4 - 2xy) dx + 3x² dy = 0; when x = 2, y = 1.

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Q: y = x y=2-x2

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Q: Consider the vector whose initial point is P(-6, 1) and terminal point is Q(-5, -3). Find the…

A: Recall: Position vector v→=a, b where a=x2-x1 , b=y2-y1 We have (x1, y1)=(-6, 1) and (x2, y2)=(-5,…

Q: State whether the given sums are equal or unequal. 20 20 Aj and ke j=1 k=1 O Unequal O Equal > Next…

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Q: Determine the radius and interval of convergence of the following power series. k X ()* 12 M8 k=1…

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Q: 16

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Q: c) 2x²8x + 4x³ - 4

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Q: Find the limit, if it exists. 8x Ilm x---x+ 2 Submit Answer

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Q: sec 2(t)- 9t2 Justify your response. b. Find the antiderivative of f(t) = s

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Q: 8) FIND THE INTERVAL OF CONVERGENCE FOR Σ (-1)" x 1=2 n2^ n

A: The given series: ∑n=2∞-1nxnn2nWe need to find the interval of convergence.

Q: The function f is shown below. What is the value of answer in simplest form. -10-9-8 5 4 3 2 11 8 6…

A: