We have In (10-x) = C-1 Σ 10 n=0 +7+1 10^(n + 1) =C- In order to find C, we let x = 0 and get f(0) - In([ 00 n=1 n10n 7) = c-([ and so C =

Q: Find L[et tsin(2t) - e-2t+3 +e-2t cos 3t]

A: BY USING THE LAPLACE TRANSFORMATION RULES  WE GET OPTION (D) IS CORRECT OPTION.

Q: Let {(=) = In ="(z +2)*(z² + 9)] f'(x) =

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Q: 2 If C = |2 -1 0 Show that (C")-1 = (C-')" -2 2 2

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Q: 1a) suppose that f is defined recursively by: f(0) = 5 and f(n+1)= 2fn + 5. Find f (1) f(2) f(3)…

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Q: Use your graphing calculator to solve the equation graphically for all real solutions 2³-6x²+x+28 =…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 1' 1 3 (e) Show that 5 k=1 k k+2

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

Q: 6. Show that, for integer s, S. s! | x25+lexp(-ax²)dx =: 2a +1

A: Note: Given proof statement has a little mistake, I have proof the actual result. First i have…

Q: L[u(t – 3) (1²4' – 9 4')] = 81e-4s 2 (s-ln 3)3 8 (s-ln 3)2 64e-3s 2 (s-In 4)3 6. (s-In 4)2 81e-4s 2…

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Q: 5. (a) Verify that t(n) = t(n+ 1) = t(n + 2) = t(n + 3) holds for n = 3655 and 4503. (b) When n =…

A: To find-  Verify that τn = τn+1 = τn+2 = τn+3 holds for n = 3655 and 4503 When n = 14, 206, and…

Q: f: ℤ675,683 → ℤ821 × ℤ823 satisfies f(x) = (mod821(x), mod823 (x)). You may use: 1=411⋅821− 410⋅823…

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Q: a/2 2. Evaluate f[(e)i-2sin(t) j+3cos(1)k]dt

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Q: Show that /(-1)-7(1) but there is Let f(x) 1 Show that /(-1) (1) but there is no number e in (-1, 1)…

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Q: Verify that det(AB) = det(A) det(B) for the following:

A: Given: The given matrices are A=1-23-231010 and B=1023-25213. First, find the determinant of A and…

Q: Suppose that an = 4" a₁x² + 2a₂x³ + 3a3x4 + 4a4x³. as 00 (i) f(n)x+2 n=0 00 (ii) Σ g(n)x¹+1 n=1 00…

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Q: 4 – x lim X → 4 5- Vx² +9

A: We have to find the limit

Q: Show that det [1 1 0 0 1 1 0 0 1 0... 0 0 1 ⠀ ... 0000 1000... 00 00 11 0 1 = 1+ (-1)"+¹.

A: As per the question we are given a matrix determinant, whose all diagonal and super-diagonal…

Q: A container contains 35 green tokens, 5 blue tokens, and 3 red tokens. Two tokens are randomly…

A: There are total (35+5)=40 non-red tokens and 3 red tokens in the container.  And total (35+5+3)=43…

Q: 17. Let P1.Pn be positive real numbers such that P1+ + Pn=1. (a) Prove the following: @P² ≥ (ii)…

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Q: dx_ -In x – 2 |x+2 X - + C x² – 4 - 4 Select one: O True O False

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Q: (15 – b) (9 – b) - z = 6. 6. För a = 1 och b + 3 saknar systemet lösningar. För a = 1 eller (4t) , y…

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Q: Suppose P(Xi=1)=pi=1-P(Xi=0),  i=1,2 if p1> p2 show that X1>( greater than equal to (st)) X2

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Q: Find F(0) if F (t) == L-! 16 82 (s+4) O 16 O 4 O 2

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Q: Σ s2 an convergent or divergent?

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Q: Show that (an) is increasing

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Q: Suppose X~N (μ,σ') then X – H - - N (0, 1) o2 O True O False

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Q: Prove that. 2/nJn-(n+2)Jne2 + (n+yjJney --- 3. end hence deduce that. 1xJn - (nti)Jnas -…

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Q: 3x'e* (x* +1)* 3e a) -+C 2(x² +1) 3e* b) 2(x² +1) +C x? +3 x +1 3 c) +C .2

A:

Q: 10. Let A = [ 8 5 6 Verify that AB = AC and yet B / C. 2 -4 -3 B = [ SINTONI 4 5 -2 3] - [37] and C…

A: The matrices are: A = 2-3-46B = 8455C = 5-231 To Verify: AB = AC