Two lines have equations L1: (0,0,1) + s(1,-1,1), s e R and L,: (2,1,3) + (2, 1,0), e R. 10. What is the minimal distance between the two lines?

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A: The trapezoid approximation of the given integral is given below.

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A: We have to substitution

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A: answer is in next step

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A: Here the area can be found by dividing the entire part in small triangles and adding the respective…

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A: nth Maclaurin polynomial for the function f(x) :       Pn(x) = f(0)+f'(0)x +f''(0)…

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A: To evaluate: I=∫2y-4y2y+2dy=-∫4y-2y2y+2dy=-∫22y-2y2y+2dy=-∫2y-12y+22ydy=-1ln 2∫2y-12y+22yln 2dy

Q: the derivative of the function at P0 in the direction of A ​f(x,y,z) = 9excos(yz)​, P0(0,0,0)​, A =…

A: Given query is to find direction derivative.

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A:

Q: Find the Taylor polynomial of order 3 generated by fat a. f(x) = x2 +x+1, a=2 O A. P3(x) =7+5(x- 2)…

A: f(x)=x2+x+1f(2)=4+2+1 =7f'(x)=2x+1f'(2)=4+1 =5f''(x)=2f''(2)=2f'''(2)=0

Q: Problem #7: (a) Solve the initial value problem (x - 1)y' - y = 16(x - 1), (2) = 0 (b) Write the…

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Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A: This question can be solved using the concept of unit tangent vector and length of vector curve.

Q: Determine the Laplace transform of 2et cos (6t - T). CO 8-4 3/3 (금) s2-8s+52 s2-8s+52 ㅇ (-) -85+52…

A:

Q: 프-3r-dx= a) 클m3x + 21+ tanx + C b)습 미3x + 21-tan'x + C Q13:J +1)(3r+2) d)흘 I미3x + 21+ tanx + C -1…

A: The integration of the integral is  (2x2-3x) /[(x2+1)(3x+2)].

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A: f(x)=x2-x-1if x&lt;13x3-4if x&gt;11if x=1

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A: Given query is to find the integral.

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Q: Evaluate the double integral over the given region. |6x sin xy dA, R. 0 SxsA, 0sys1 R. O A. 6x 兀 OB.…

A: We will evaluate the double integral.

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A: Given query is to find series converges or diverges.

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A: Integral Test : Suppose that f(x) is a continuous , positive and decreasing function on [k,∞) and…

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Q: explain

A: We will check if the fundamental theorem of Calculus is applicable.

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Q: 4 Which formula would be used to calculate the trapezoid approximation of L dx using five…

A: We have to use trapezoidal rule. Option B is correct.

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A: Surface Area of the solid generated by revolving about the y-axis ,S = ∫x=ax=b 2πx 1+dydx2 dx

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A: 2) as per our norms we have to write one question at a time kindly repost remaining questions.

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Q: 1 Determine the values of a, b and c if: 2(a,b,4) +(6,8, c) – 3(7,c,-4) = (-24,3,25)

A: We can solve this as follows:

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A:

Q: V. ASSESSMENT (Time Frame: (Learning Activity Sheets for Enrichment, Remediation, or Assessment to…

A: Given