k E R and f(x, y) = x² + y² + kxy

Q: Find a unit vector u in the direction of v. Verify that llull=1 v=(-5,-3)

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Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the b...

A: We have given∑k=0∞(67)k+3

Q: (nx)dy/dx+2y=xy^(n+1) where n is constant, solve using linear equation diff eq

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Q: - Let y=f (x) + C be the antiderivative of F (x) = determine the value of C (use 3 decimal places, a...

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Q: minimize z=4x+6y subject to: 3 0 y > 0

A: We are going to solve the give. Problem by graphical method.  In the shaded region, the linear funct...

Q: Evaluate by any applicable method. S sin (y) cos" (G4) dy None of the choices. Please refer to my so...

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Q: Last summer, a DAVDECO electrician conducts a record of the electrical voltage supply readings withi...

A: Answer 1:

Q: 4.Determine the convergence of the following series. For a series replace sign, if it converges, Als...

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Q: Evaluate the integral. 6 dx 16

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Q: Suppose that {a, } is a monotone sequence such that a, 10 or increases- in this case we can't say w...

A: We need to choose correct options.

Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

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Q: Evaluate by any applicable method. 1/2 5-x So dx 4x2+1

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Q: . Antibiotic treatment. A biologist has a colony of a toxic strain of bacteria that covers 500 mm² i...

A: We have to find the area of the bacteria coloney as a function of time at the gives instances.

Q: Find an equation of the tangent line to x^2y^3 −y^2 +xy−1=0 at (1,1).

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Q: Find the directions in which the function increases and decreases most rapidly at Po. Then find the ...

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Q: dx Evaluate: Jo JA4-x² ' o V4- O 1/6 O T/2 T/3 O None of the choices ООО О

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Q: Express the repeating decimal as a fraction. 0.343434...

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Q: Find the general term of the sequence, starting with n = 1, determine whether the sequence converges...

A: consider numerator series : 3,4,5.........we can re write this as 2+1, 2+2, 2+3 ,............since n...

Q: Determine the limit or show that it does not exist. (x- y)2 + 2(x - y) – a2 – 2x (a) lim

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Q: 6. Se¯*tane¯*sec?e¬*dx

A: To evaluate: I=∫e-xtan(e-x) sec2(e-x) dx=∫tan(e-x) sec2(e-x) (e-x)dx...(1)

Q: #24 and 26a

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Q: Rewrite the integration in terms of u. 1 x cos 10rx² dx = COs u du Apply the constant multiplication...

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Q: – ydx + (x ++ Vy )dy = 0

A: Given that Diffrancial equation-ydx+x+xydy=0Solution:-ydx+x+xydy=0x+xydy=ydxdxdy=x+xyydxdy=xy+xyydxd...

Q: The function k(x, y) = e cos(2x) has a critical point at (0,0). What is the value of D at this criti...

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Q: a. Express dw/ dt as a function of t, both by using the Chain Rule and by expressing w in terms of t...

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Q: an+1 n -to determine if the sequence An is strictly increasing or strictly decreasing. Use the ratio...

A: In this question, we need to check whether the given sequence is strictly increasing or strictly dec...

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by ...

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Q: (a) A curved wedge is cut from a cylinder of radius 3 by two planes. One plane is perpendicular to t...

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Q: Let f (x) and 8 (x) be antiderivative of h (x), The which of the following is true? A None of the gi...

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Q: dx 9(+x²)' tan 2 2 none of the choices Option 3 3x tan + C tan 2 O Option 2 Option 1 +

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Q: Question 1 f 8(x) =3x2-4x +5 ; G(x) =x-2x2+5x , then G is the anitiderivative of f. A True B False Q...

A: topic - integration

Q: (a) Fully factorise the following equation x + 3x?y + 2xy² + 6y3 Find the coordinates of the centre ...

A: We factorise the given equation and find the center of the circle and radius in b part. Follow 2nd s...

Q: Title: Differentiation Rules Tasks: Solve the following problems completely and accurately. Use the ...

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want...

Q: Find the equation of the tangent and normal line to the following curves at a given specified point....

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Q: Find the area of the region that lies under the graph of f over the given interval. Please solve usi...

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Q: 4. у %3D х6 - 3x + 5x2 7 2 4 6 8 5. у %3D (x + 10) (2х - 5) 6. у %3D (x3 + 1) (3x2 - 1) 7. у %3D 5x ...

A: 4)y=x62-3x44+5x26-78Differentiate w.r.t.x using power rule.dydx=6x52-3*4x34+5*2x6-0dydx=3x5-3x3+53x

Q: For the functions w = 8x + 3y, x= cos t, and y = sin t, express dw as a function of t, both by using...

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Q: 17. y = e"(p + p\p)

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Q: (4x3-6х) dx 3. S x*-3x²+2

A: ∫4x3-6xx4-3x2+2dx we know that∫f'(x)f(x)dx = ln|f(x)| +cf'(x) =4x3-6x , f(x)=x4-3x2+2

Q: Determine the sum of the following series. NOTE: Enter the exact, simplified ansuwer as improper fra...

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Q: " sin²(x) + sin(x) xp- cos²(x) To evaluate the using basic formula of integration (without using sub...

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Q: 12. Simplify. 6m? + 13m – 5 9m? – 4 8m? + 16m – 10 6m2 + m – 2

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Q: 2. A rectangular field is to be enclosed and divided into four equal lots by fences parallel to one ...

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Q: ,2 + 5х + 4 f(xæ) х — 1

A: For x-intercept substitute f(x)=0⇒x2+5x+4x-1=0⇒x2+5x+4=0⇒x2+4x+x+4=0⇒x(x+4)+1(x+4)-0⇒(x+4)(x+1)=0⇒⇒x...

Q: Determine whether the series converges using the limit comparison test. 3k2 – 2k + 7 Σ 12k6 + k – 12...

A: We have to prove that the above series converges or diverges.

Q: 43 part a b and c

A: Topic:- function and it's Derivatives

Q: Find the indefinite integral. sin 60 v cos 60 de Step 1 To solve the integral | sin 60 v cos 60 d0, ...

A: We can solve the indefinite integral as below.

Q: Y= (5x1)"(4x²-) こト

A: Given that the relation between x and y.. And use the product rule of differentiation  and then simp...

Q: 9. Prove the following algebraic identity: (a - b)(a? + ab +b?)=a' -b'

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Q: 8. Svay y3 y²dy 2-

A: We have ∫y2dy2-y3