Eliminate c from the equatia cxy + c²x + 4 = 0. O x* (y')? + x?yy + 4 = 0

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A: We have to find the area between the parabola y=x2-1 and the line y=x+5 .

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Q: I = -2+3s z + 4 1. Consider the lines defined by the equations l : x – 2 = y – 1= and l2 : y = -1+ s…

A: Given:  l1= x-2 = y-1 = -z+42=tl2= x+23 = y+1 = z-2-4=s

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Q: Find the gradient of the function at the given point. 2 = In(x2 – y) - 9, (2,3) Vz(2, 3) = Need…

A: This is a problem related to derivation. Please follow the procedure given below for solution.

Q: 1 Evaluate lim Gnx x→1+ 'Inx х-1

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Q: Eliminate* the arbitrary constants c1 and c2 from the relation y = cje-2* + cze³* у" -у — бу %3D 0 O…

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Q: Determine the convergence or divergence of the sequence with the given nth term. If the sequence…

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Q: Apply Theorems 5 and 6 to find general solutions of the dif- ferential equations given in Problems…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: - 2 Evaluatelim x- 8x2-7x-8 O 1/9 O 27 O NONE OF THESE 1/12

A: To evaluate: limx→8x3-2x2-7x-8

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Q: Consider the following function. f(t) = 4t + 5 Find its average rate of change over the interval [1,…

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Q: 1. Given z, = 5 cos 377 +i sin 37 and z2= 37 +i sin 2 find z,z2 where 0se< 2x. cos 2 2 37 +i sin 2…

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Q: (e) Alternating Series Test: Σ (-1)"-2 3n + 3n

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: To solve the following problem

Q: 4. S ( 12 x³ + 15 x - 20 ) dx 5. S 10 x2/5 dx 6. § 3 ³V x8 dx 7. S ( 8 + 2 dx x3 x4. 8. S ( 2x³ -…

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Q: Find T(t) and N(t) at the given point. r(t) = (t² – 8)i + tj; t= 8 %3D T(8) = | %3D N(8) =

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Q: Find the area of one petal of the rose curve r = 3 cos 30.

A: Let's find.

Q: 5. St V1-t dt

A: We solve this integration by substitution method by putting                         1 - t3 = u…

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Q: Find the direction cosines and angles of u and show that cos a + cos B + cos? y = 1. (Round your…

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Q: a) Compute the area of the shaded region by "counting" the squares on the grid in the given region.…

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A: Find your answer below

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: Solution is given below:

Q: Choose the rule that you would use to most efficiently find the derivative of the function 3 f(x) =…

A: The given function,   f(x)=32-x3

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Q: Find an equation of the plane through (0, -9, – 1) that is perpendicular to the line x - 2 = 3t, y +…

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Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). %3D v= (0, 6) %3D b =

A: Explanation of the answer is as follows

Q: Consider the following. u = 3i - j - k, v = -i + 5j + 7k %3D (a) Find the projection of u onto v.…

A: Given :  u=3i-j-kv=-i+5j+7k   To Find: a)Projection of u onto vb)Vector Component of u orthogonal to…

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Q: (0,0,0) (1,1,1) C2 C.

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Q: Find the following. u = (0, 1), v = (5, -3) (a) |u|| (b) ||v|| (c) |u + v|| (d) |u| M (e) U + V (f)…

A: We can solve this as follows:

Q: What is the value of the definite integral 61 +2 dt?

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Q: Use the formula k(t) ||F(t) × r"(t)|| to find k(t). ||r(t)||° r(t) = 11 cos(t)i+11 sin(t)j+6tk K(t)…

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Q: ALL WORK Solve the triangle, if possible. If the triangle represents the ambiguous case, solve for…

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