n-1 Show that : [(n) = Ln dx ,n > 0 %3D 1 Show that if n> 0, m =,(n – 2) , then : 2m + 2 3* r (n +3) O Prove that = 2.5.8. 11 . (3n – 1)\T ... | 72

Q: Does e + z? have "fenetely mony gores in E explain.

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: k Show that L{sin kt} = s2 + k2'

A: Solution

Q: 1. The coefficient a, of the Fourier series of the periodic function f(t+6) f(t) (2t 0<t<2 f(t)=o…

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Q: x +1 Evaluate : dx. (1 +x e*)

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Q: 64 2) Find the value of "k" on [0,4] such that the area of x*dx is half the area of x*dx: 3

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Q: Evaluate fff. 5y²dV where E is the reqion below x + 3y + 6z = 9 in E the first octant.

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Q: + tan dy 37 Ify = tan -1 -1 1 2 x +5x+7 1 2 1 2 1 2 x² + x + 1 +... to n term.

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Q: Question 2 x+1 Let p be a real number and define y = d: for x>1. dy _ -2 py ( a) Show that dx x -1

A: Hi , i have solved 1st part.for 2nd part repost your question.

Q: 1 1) [ (tan³ 0 + tan³ 0) e-tan º d0== 2 (-1)" n! (In x)" dx= (m + 1)"+1 ·

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 5. Find the Fourier series of |x| of period 27 and evaluate the sum 1 1+ 32 1 +... 52

A: 5)

Q: Choose the statement below that is FALSE (only 1 is false) and piein why it is taise. \a (x+ 2)² 6 #…

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Q: Use mathematical induction to prove that cos(x+n) = (-1)" cosx where n≥le J*.

A: Mathematical induction is defined as a mathematical technique that is used for the expression,…

Q: Evaluate f x(x- 1) dx | c. (x + 1) -x + 1) +C D.x – 1) -- 1) +c x(3 35 1)z (x- | | 35 35 35 |

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Q: (3) Prove that n=2²°² is a square. 2K+1 where K = 1 $ (n)

A: This follows from the definition of euler Phi function

Q: (n+1)x*! – x* . cos ((n+1)x) dx, where n is 4

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Q: Evaluate O - f 1 1+¹/3+C 0 3 O dx 1+x¹/3 2²/3 In 1+¹/3+C 0 3 - 3x¹/3+3 In 1+¹/3+C 222/3 ○ In 1+¹/³+C…

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Q: Use the Error Bound to find a value of N for which error (TN) ≤ 10. Let K₂ be the maximum of If"(x)]…

A: Given ∫257xdx, We have to calculate N by using error bound.

Q: Fourier series f(x)= x sinx 2 xe (7)

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

Q: EVALUATE -dx + 144 ,2 O x – 12tan-1 12 none 1 -sin' 12 x – -1 +c 12 O x – tan-1 12

A: We have to evaluate  ∫x2x2 + 144 dx. We know,  ∫1x2+a2dx = 1atan-1xa + C      (where C is constant…

Q: Question 4. Using the Mean Value Theorem, prove that (a) 1 1 dx < 1. a2 )5 32 (1 + (b) 4 < Vx2 + 3dx…

A: Given,a) to prove132≤∫011(1+x2)5dx ≤1mean value theoremIf 'f' is continuous on [a,b] then there…

Q: What is the complex Fourier series of the function f(t) = cos t? Hint: if you're confident, you can…

A: We find the complex Fourier series of the function f(t)=cos(t).

Q: ? Suppose that * f(3) = 1, and f(x) > 0, and f(x) < 0. Is it possible that f(2) = 3 4

A: Given fι 3=12  and    fιx&gt;0and fιιx&lt;0 . it is possible that fι2=34let g3 =  fι 3=12    ,…

Q: n lim >(sin (2mx;))Ax over [0,1] i=1

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Q: s** dx 13*+4* O -1.679 O -1.679 O -0.1132 O ×0.1132

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Q: 21) f(x)=47x A) (4 ln 7)47x Write summation notation for B) (7ln 4)47x x(In 2) C) (In 4) 47x x(In x)…

A: Finding the derivative of f(x)

Q: x² + 9 dx J x2 – 1)(x² + 4) | In \x + 1| + In |x – 1| +; tan-1 (-) + c -In |x + 1| - In |x – 1| -;…

A: Topic:- application of integration

Q: 9- a) b) C) e) The Fourier series of the function f(x) + 2 8 0 -4 = 8, -4, -π<x<0 0<x<T at the point…

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Q: 10V dx (1+x³/2)² 1 Evaluate Evaluate J. So Vē cos (03/2) de I

A: (1) Let t =…

Q: Show Recurrence that the solution to T (n) = T (2n/3) + 1 is Θ( log2 n)

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Q: Question 12 Prove that 1(2) + 2(3) + 3(4) +.+ (n – 1)n n(n-1)(n+1) . for n > 2. 3 ... Edit View…

A: We will prove the given statement.