Problem 18.11. Let F: X ×Y → Z. We say that F is continuous in each variable separately if for each yo in Y, the map h:X Z defined by h(x) = F(x × yo) is continuous, and for each ro in X, the map k : Y Z defined by k(y) = F(ro x y is continuous. Show that if F is continuous, then F is continuous in each variable separately.

Q: Use the method of variation of parameters to find the general solution of the differential equation ...

A: We have to find the general solution of given differential equation by the method of variation of pa...

Q: 3. Find the derivatives of y with respect t x: a) y = xe* – e* %3D b)' y = e(tx+) c) y = e*(sin x + ...

A: To find- Find the derivatives of y with respect to x. y = xex - ex y = e4x+1x y = exsinx + cosx y =...

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Q: Solve the following Laplace Transform of Algebraic Expression: 5. Finf the L t?e-3t ? Show Solution.

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Q: Determine whether the given series is convergent or divergent. 5" + sin? n (a) ► 3n – | sin n| - n=1...

A: a) The given series is ∑n=1∞5n+sin2n3n-sin n. The square of any real number is always greater than 0...

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Q: Using Max-min composition, find relation between R and S: Уг Уз X1 [1 1 0 0 0 1 Z1 Z2 У1 [о 1 S = y2...

A: Solution 2. Given that               y1y2y3R=x1x2x3110001010 and                z1z2S=y1y2y3011011 L...

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Q: +00 nyn n² + + 2-n n=1

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Q: 3. Find the derivatives of y with respect to x: a) y = xex - e* %3D b)' y = e(4x+;) c) y = e*(sin x ...

A: To find- Find the derivatives of y with respect to x: y = xex - x y = e4x + 1x y = exsinx + cosx y ...

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A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts fo...

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A: Sequential pairwise voting does not satisfy the Pareto condition. All other systems are given in the...

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Q: (1) If A is diagonalizable then cA is diagonalizable for any constant c. (i1) If the characteristic ...

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Q: (b). A club has 5 freshmen, 6 sophomores, and 7 juniors. How many committees of 4 people from at lea...

A: No. of Freshmen = 5 No. of sophomore = 6 No. of juniors = 7 Total = 5+6+7 = 18

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A: Fourier sine series  of the function f(x) in the interval 0&lt;x&lt;L f (x) = ∑n=1∞  Bn  sin  nπx L ...

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A: Geometric series

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Q: Find o (in degrees).

A: Given,       

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Q: 3n + 2n + 1 1, test for convergence or divergence, using each test ermining Convergence or Divergenc...

A: We have to check whether given series is convergent or divergent.

Q: Find the coordinate matrix of x in Rn relative to the basis B'. B' = {(4, 3, 3), (−11, 0, 11), (0, ...

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Q: 18s-13 Find the Inverse Laplace of F(s) s2 +7

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Q: 1. Let f and g be continuously differentiable functions. PROVE: div(fvg -g v f) fag gAf %3D Hint - U...

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Q: 1. Let k be any positive integer. Use induction to prove that for every integer n > 0, kn+2 + (k + 1...

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Q: r – y, y(0) = 0 dr (b) Solve the initial value problem exactly evaulate at y(2).

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Q: Determine the convergence or divergence of the following series. Use Integral Test.

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Q: b.) Show that if a and b are positive integers where a is even and b is odd, then (a,b) = (a/2, b). ...

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Q: -Sy =D0

A: Given that y'''-8y''+6y'-5y=0. We have to find a method so that we can solve the above equation.

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Q: Link between every sequences and this specific properties {1n(n? +n+5]} is A. geometric The sequence...

A: We will use concept of sequence to verify the nature of sequence. 

Q: Datormine whethe each of the prlowing series waverges or diverges usIing inly the anvergence tests. ...

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Q: 1 (iv) f(x) on [-}, 1]. x* + x + 1 x + 1 (v) f(x) on [-1, }). x? + 1 (vi) f(x) on [0, 5]. x? - 1

A: Given: (iv) f(x)=1x5+x+1, -12, 1 (v) f(x)=x+1x2+1, -1, 12 (vi) f(x)=xx2-1, 0, 5 To find: Maximum and...

Q: 2. Use the Integral Test to determine if the series Σ (n+2)¾ 1 n=1 converges or diverges.

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Q: 4. Use mathematical induction to prove that Vn E Z* u {0}, []²=o(2i + 1)! > ((n + 1)!)**. n+1

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Q: 26. Write the equation of the line pas sing through (2, - 4) and parallel to the line y Зх -2.

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new ques...

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Q: 4. Use mathematical induction to prove that V n E Z* U {0}, [I²-o(2i + 1)! 2 ((n + 1)!)**. n+1

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Q: Which of the following statements are always true? (i) If A is a 3 × 3 diagonalizable matrix then A ...

A: Linear algebra.

Q: 4. Give an example of a pair of dihedral groups that have the same number of conjugacy classes as ea...

A: We know that Dihedral group is denoted by Dn. Its order is 2n. Here, to find the pairs of Dihedral g...

Q: Find Im(z) if z(8 + i) = 7+ (384 + 448i)

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