Consider the surface defined by the equation z2 = 2x² + 4x - 6y? - 2y+ 1. %3D Find a set of parametric equations for the line normal to the surface at the point (2, 1, -3).

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

Q: 1: Find the arclength of the a, curve V1 - x, 0 < x s 1, Is the given series 2 - 1 + 2 1 + 4 ... a…

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first one. If you…

Q: fi(x) 1 A = {fi, f2, f3} c F(R) and f(x) = f:(x) = |x+ 1| PROVE: A is linearly independent. (A L.I.)

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Q: III. Graph the following functions: 4. y lIn(x-3) 5. y= In(x-1) 6. y= In Vx-1

A: Consider the functions 4.   y=|ln(x-3)|5.   y=lnx-126.   y=lnx-1

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A: Given problem:- Find the absolute maximum and absolute minimum value of f of the given interval.…

Q: | Consider the DE: x²y" – 4xy + 4y = 0. A) Verify that y = c1x* + c2x is a solution of the DE. B)…

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Q: A scientist has discovered a new strain of bacteria. The bacteria culture initially contained 1,000…

A: Given problem:- A scientist has discovered a new strain of bacteria. The bacteria culture initially…

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Q: Think of four random integers q, r, s, and t selected from 0 through 9. Let a1 = 0.qrst, where q, r,…

A: let as consider four integers q,r,s,t from 0 to 9 then we get a1=0.qrst=0 now if we select four more…

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Q: -2n f) S“ cos 2x dx g) S et² t dt h) S x sin(x²) dx

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Q: Q2/ Complete the following table to find the values a , b,c and s y A -1 2845 308 3162 S 3544 a 2…

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Q: y" + 3y' + 2y = 12x* %3D y" + 4y' + 4y = e¬* cos x

A: As per the guidelines I am supposed to do the first problem in case of multiple problems. So here I…

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Q: Espar Find an equation of the hyperbola having foci at (-2,-V40) and (-2, 40) and asymptotes at y3 1…

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Q: The volume of the solid under the plane 3 x+ 3 y -z=0 and above the region enclosed 23 by y=2 x and…

A: y=2x and y=2x22x=2x2x2-x=0x(x-1)=0x=0, y=0x=1, y=2

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Q: 8. Evaluate the integral by using trigonometric substitution 4x-x2

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Q: 7 For the function f(x) = x – , find all values of c in the interval [4,6] that satisfy the %3D -…

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Q: The integral 5x – y dA =49 if R R={(x,y): 2<x< 4, 5< y < 6 } Select one: O True O False

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A: Topic = Triangle

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Q: Write the equation of the hyperbola in standard form. (-1,7) (-1.5)

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Q: i) The area of the surface obtained by the rotating the curve y=V 36-x, -3<x<3 about the x- | axis…

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

Q: (a) Use differentiation to find a power series representation for fx) = (3 + x)2" Σ 00 n = 0 What is…

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Q: b. f(x) = xe-*, g(x) =; -1<x< 5. Show in a single space. 2x

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Q: Use the Ratio Test or the Root Test to determine the convergence or divergence of the series. 1 1 1…

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