Question 13 Evaluate L{r³e3r+S, 6e5 (A (s– 3)4 6 (B) s*(s– 3) 6e5 s4(s- 3) D s4(s - 3) (s– 5)

Q: D Exponential Shifting Theorem 4 (D° + 4D°-3D - 18)4=24x°e-3× t 4D²-3D - 18)y = 24 x°e¯*

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Q: 4 F(s) 3s2 + 1 s - 3 1+ (8 – 3)² 1 F(s) = (s – 3)5 F(s) = s2 + 2s + 1'

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Q: 1. F(s) = 16/[s(s²+4)] 2. F(s) = (8s + 11)/[(s-4)(s²+9)]

A: We have to solve by inverse Laplace transform.

Q: 1 "F(s) = a. s² – 2s+17 s-1 O b. F(s) s(s? – 2s+5) 1 OC. F(s) s² – 2s+5 s-1 O d. F(s) s(s? – 2s+ 17)…

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Q: 1 F(s) F(s) s2-6s+34 s2 +4s+4 s2-4s+53 s2-6s+9 This option This option

A: Laplace transform

Q: 7 (a) F(s) %3D (s+3)³ 2s – 3 ( (b) F(s) = s2 + 2s + 10

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Q: 9. h(x) = 9x-3x'-12x – 10x-7 %3D a. h(x) → -∞ as x → -o and h(x) → -00 as b. h(x) → ∞ as x→ -00 and…

A: As h(x) is polynomial, it is always continuous . h(x)=9x4-3x3-12 x2-10x-7 h(x)=x4 (9-3x-…

Q: [2 7 10 ] cc 1 -2 -1 3 d. Fi 10. -6 3 -6 -2 lir | е. If is 2 1 -7 5 -6 (12. 1 -2 -4 -1 7 -4 in 7 -…

A: Actually we can use here four variable with three equation and use row operations to get the answer

Q: L(e-3t)= %3D 1 s2- 3 1 .bO s2+3 S-3 1 .dO s +3 1.

A: We can solve it by definition of Laplace method Consider Le-3t = ∫0∞e-ste-3tdt=∫0∞e-(s+3)tdt=…

Q: S(s²+2) (s+)(s+) (S+2) Cs+D (S2+1) A %3D (S+1) (S+a) 12 3 2(5+1) %3D 5(5+2) [ %3D (s+2) (S*+1). B =…

A: Answer

Q: Example -3 .2 Evaluate I (x+ 2y – z) dx dy dz I (x + 2y – z) dx dy dz - 2 SLE + 2xy – xz dy dz - 2…

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Q: (-1)"-1 5+ Vn 1. n=1 3 2. 1+νη n=1 5+ νη 1+ νη 3. n=D1 1 2η 4. 3+ νη n=D1 1 5. I (-1)°, (-1)*.

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Q: Question 47 dy Calculate dr . You need not expand your answer. 2x +2 4х — 5 0 2(4х — 5) — 4 (2х + 2)…

A: We have to find derivative

Q: Excercies 1. Find L-1 (,2) . 2. Find C-1 (-올 + ). 3. Find L-1 (2, +2). 4. Find L-'(16). (2s+7) s2+16…

A: As per guidelines of Bartleby , I am able to do only first three part of this question. If you want…

Q: s³-2s²+5s-9 R(s) = %3D s2(s+3)(s+1) 3s+10 W (s) %3D s(s-8)(s-6)²

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Q: x-4x+7x-9 r x-3 A. C 4x +3 In Ix-31+ C 3 + 4x + 3 In Ix-31+ x3 x2 + 4x + 3 In Ix-3 I + C 2. *+-4r+3…

A: Topic = Integration Correct option = B

Q: s+3 L[e-3t cosh( 3t)] = %3D (s-3)²–9 True False

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Question 3. Show that n3 + 4n2 +1 O(n²). %3D n+3

A: See the attachment

Q: L{(1+t")e 3t)= (1+)() n! sn+1 -3 1 n! s-3 sn+1 1 n! s+3 (s+3)"+1 n! 1+ sn+1 )() (2) s+3 (1)

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Q: 38 4. Find L-1[e+7)]. '(2s+7 s2+16 5. Find L-') 6. Find C-1e (s–3)(s+1) 7. Find L-1 24e-5 82-9

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Q: st4 (i) F(s)= (s+2)(s+1) st6 (ii) F(s) = (s+1)(s+3) s+6 iii) F(s) =' s(s+3)

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Q: 9. between z = -2.09 and z = 1.72 Area: 10. to the left of z = -1.27 and to the right of z = 2.86

A: To find the required areas we use Standard Normal table.

Q: Part (b) 7s +4 Find L-{F(s)} (s + 4)° Let F (s) = s2 + 4

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Q: 5 0.6 0.1 Apply Gershgorin's theorem on B = -1 6. -0.1 1 2

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Q: السؤال 9 L(e-3t)= .a O s2 -3 .b O S - 3 1 .c O s2+3 .d O s +3 1. 1. 1.

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Q: lim/ 63-64 t*-7t+12 い+ E-4 6²- 34 -4 j + 3(t-y) In(t-4)£ ニ

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Q: 5s +3 3) Find L'{Y(s)} where Y(s) = (s+1)(s+2)(s+3)

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Q: 1 3-2s Compute y(0). Given: Y(s) = 3-4s +49 Round-off to 2 decimal places. Answer: -2.25

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Q: L(e 3t) = 1 .a O s²+3 1 b O s +3 1 S-3 .d O s2 – 3 1.

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Q: t u(t-2) L. 31 O e3-2s (s+3)² 1. 2 s+3 e-2s 1 2 (s+3)? s+3 లాఓ-5 (x+3) -6-2부 2. +. (s+3)2 +3 (6+3)2…

A: The solution is given as

Q: 00 n + 1 is divergent. If we multiply any constant (labeled as h)to the n + 1 such that n + 2 n=1 n…

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Q: +2x+3 x+3x +9x - In Ix3 + 3x2 + 9xl + C C In Ix³ + 3x² + 9xl + C 3. BIn Ix3 + 3x² + 9xl + C D2 In…

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Q: -3 3. Find AB where A = 4 -2 L3 2 4. What is x in the equation 2x - 3 -1] [2 -1 5 and B = 1 3 2 14 1…

A: topic- matrices

Q: 7) F(s)= 1 s² + s/2 Ans. f(1)=2-2 e 1/2

A: We have to find the inverse Laplace transform of the function F(s)=1s2+s2 .

Q: 7) -U(X-2)(x+3)" (5x-1)(7x+ 2) 3х+13 6) 57 In7x+2+c) (ans.: In 5x 2х -3 7)Sー (ans.: -Im,x-1+ Im,x-2-…

A: ∫1ax+b dx =1alnax+b+C Note :As per our guidelines , we can solve first question .Please repost…

Q: 2(1 – e-5s), e-6s Y(s) = %3D s(s +1)? * (s + 1)² (8+1)²

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Q: s 1 s(s+ 1)² -1 +et+2te-t Option 1 2+te-t Option 3 - 1 + e-t2te-t Option 2 -2+te+e-t Option 4

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Q: -5 #2. Suppose that S„ƒ(x)dx= 6 andS²,g(x)dx= -4. Find S°,[3f(x) – 0.5g(x)]dx.

A: To evaluate the given integral apply the following rules.

Q: Transforming S Ⓒ √ 2²-22²2 =2 A -dz 1+z² z²+z B -dz 1- © S с © S D N dx using miscellaneous…

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Q: Example 10.20. Using Milne's method find y(4.4) given 5xy + y²-2=0 given y(4) = 1, y(4.1) = 1.0049,…

A: Solution : Given, 5xy'+y2-2=0 ⇒y'=2-y25x Table of x and y x 4 4.1 4.2 4.3 y 1 1.0049 1.0097…

Q: (k) E(-1)"-1. n+1 n=1 Vn +1- Vn – I (1) n=1

A: The given problem is to determine whether the series is converges or diverges using the appropriate…

Q: 11) F(s) = (s+2)² +n²z² 12) F(s) = (s+3) +1 2(e-e) 13) F(s) = 14) F(s) = 16) F(s) = 17) F(s)- s +2s…

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Q: L(3+e2^)²= 9. 6. 1 - S- 2 .a O s- 2 6 1 - s- 2 .b O S-4 S 3. 6 1 + s-2 s-2 9. 6 + S- 2 - .d S S-4 1…

A: Given that L3+e2t2.It is required to find the Laplace transform of 3+e2t2. I is known that Laplace…

Q: y 3.0아 (1, e) 2.5 2.0아 y-e* 1.5 1.0 y = xe*2 0.5 -1.0 -0.5 0.5 1.0 1.5 2.0

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Q: -1 2 and y = 1 3 -y 6. x = -3. Compute (E) y. (-1)

A: To find ((x.y) /||y||^2) y For the given vectors.

Q: (s-1) Find L-1 O [(s+3)(s²+2s+2)]

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Q: S. (e3* + 1) / (e3* + 1)²– 4 Evaluate: e™dx e sec -1 6. 3x +1 -+C 2 A e +1 e 3r B sec -1 +C 2 C None…

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Q: 1 s+1 3) F(s) = 극 (을. s2 s2+1

A: Our guidelines we are supposed to answer only one question. Kindly repost other question as the next…

Q: pon homogencous Lincar ODE y'+3y = 18x² yro)=-3 y'@)=0 And exace sol'n 5.

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Q: *y" - 9xy' + 16y = 0

A: Given: x2y"-9xy'+16y=0                    (1) Let y=∑n=0∞cnxn  be a solution of (1)  Then,…