sinh 2 .a O 3s2 –4 9s2 – 4 6. s2 – 4 2s²-4

Q: - ) s2 – 4 2s+6 What is L -2 cos 2t-3 sin 2t A.

A: find the inverse laplace transform of L-1-2s+6s2-4 we can write the function as…

Q: 3. Find L{2t²e* cosh t}. 2 ans: g" (s+2)'

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Q: 2 s2+4 cos2t a o sin2t b O sinh2tcO .C cosh2t d O

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Q: 16s Ans. 1) f(t) = 4t sin 2t (s2 + 4)2 %3D

A: according to the guidelines I am answering only first question. rest of the question are similar to…

Q: L {(t + 3) sin 2t } = Select one: s2 – 4 (s² + 4)² s2 + 4 s? – 9 + (s² + 9)² s2 + 9 6s (s² + 9)² +…

A: Lsinat = as2+a2. If Lft = F(s) then Ltn f(t) = -1ndndsnFs.

Q: sinh (Inx+ Iny)= Select one: x2-y? 2xy O 2xy x²y²+1 2xy Zero None x x²y? -1 2ху

A: Here find the value of sinh(lnx+lny).

Q: ft) = cos 2t + sin 2t + cosh 2t + sinh 2t 2s? (s+2) А. (s2 +4)(s2 -4) 2s? (s-2) С. (s2 +4)(s2 -4)…

A: We find the Laplace Transform of  f(t)=cos(2t)+sin(2t)+cosh(2t)+sinh(2t).

Q: If e/2i =sin2 then z = - 2 In(sin2) + 4k t – 2i In(sin2) + 4k T

A: Equation can be solved by taking natural log both sides

Q: 2s 18\ L. L-1 s2 +9) a. cos 3t - 6sin3t ẩj2cos 3t – 6sin3t c. 2cos 3t - Rsin3t d. cos 3t – 2sin3t

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Q: L' (s²+4)(s²+9) 3 f cos(2a) sin[3(t – æ)]dx O b) cos(2t) sin(3t) c) None of these 1 * Só cos (2a)…

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Q: In( cosh(3x)+sinh(3x) )= Select one: O- 3x 01 O None O 3x O3 sinh(3 x +

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Q: 2.L cos v5t 3V5 sin v5t 5 8s – 3 a. s2 +5 8s + 3 b. 52 +5 8s – 3 2-5 С.- d.none

A: NOTE: Refresh your page if you can't see any equations. . use the Laplace rule

Q: What is L - 2s +3| ? 5s² – 10] A. -2cos 2t –3.sin 2t 8. cos ār -sin v31 sin 3t 3 C. cost --sint 2 D.…

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Q: Lim Sx- 3 大ロ3 2メー5メ-3 /50it was す S4 2. the - sint cost Lcost 1 sint cost 14 Onot of the above

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Q: 7. 3s+4 L-1{ s²+4s+5- 2t a. e²t (3 cost - 2 sin t) b.e-2t (3 sint 2 cost) – c. e2t (3 sint 2 cost)…

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Q: 3. L sinh %3D 4s .a O 4s²-9 3s .b O 3s2 - 4 12 .c O 16s?-9 9s 9s2-16

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Q: 12+4x +3= 0 New root.s ニ Sum t. product Simpity SOR POR using (*i t B) こ

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Q: Q2-4 * Amount Equal sin(2x) J (D²+D+l)° (5sin(2x)–12cos(2x)) (5sin(2x)–12 cos(2x)) (5sin(2x) +12…

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Q: lim In(12x+ 1) csc(4x) A) 0. B) 1. C) е. D) 3. E) 0.

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Q: sinh(1+ Inx)= Select one: Zero e?x² – 1 2хе e Inx 2 None e?x²+1 2xe x² +1 O 1+ 2x

A: We need to simplify the following expression sinh1+lnx

Q: 3t L[e* (6 cosh(3€) – sinh(5t) ) O A. 6. (s – 3)* – 9 (s – 3)- 25 OB. S-3 (s – 3) (s- 3) - 25 OC.…

A:

Q: In( cosh(8x) - sinh(8x)) - In( cosh(9x) + sinh(9x) ) = Select one: O zero O 17x O None Ox O 8X O- 17…

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Q: L[2 sin² 3t] s2+9 1 S s2-36 3 s2–9 1 s2+36 |

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Q: Evaluate L{3(sin² 2t )} 24 24 24s 24 а) s(s² + 4) b) d) s(s² + 16) s(s² + 16) s(s² – 16) a O Option…

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Q: 12 5. Evaluate: L L g?-4s-5 A• 4e sınh 3t 2も 8. (2e2+ sınb 3t -C. 4p 2t sinh 3€ -2t D. 1ae sinh 3t

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Q: What is L 2. s² -7 s -36 cosh 3t +sinh 9t 3. B. cosh7t +sinh 6t C. 5cosh 10t + sin 2t D. s 31 +sin…

A:

Q: &. y = -2 co0(2 -) 7. y = -3 sin 2r + 9. y = 4 sin ( mX 11. y = 3 cos ( TX 2) + 5 12. y = 2 cos (2nx…

A: I have provided solution in step2.

Q: Find L-s+9)2–36 e- 76- –9t sinh6t 16 e-cosh6t 6. 16 e "cos6t 16 9t

A:

Q: -2s+9s2-8s+18 Find L-1 s(s²+4)(s+1) O (2- 5e +3 sin 2t) O (3 - 5e-t + 3 sin 2t) O (1-3e-t +3 sin 2t)…

A:

Q: Find L{(t- 1) (2 5 sin 3t)}. 30s 52+9 15 15 s2 (s2+9) s(s² +9) 15 2 g2+9 30s 15 15 s2 (s²-9) s(s2-9)

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Q: } Find L Find L-1-2s³+9s² – 2s+12 s(s²+4)(s+1) S (1 — Зе + 3 sin 2t) (4 – 5e + 2 sin 3t) о (3 — 5е +…

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Q: GUESTION 3 dy Fmid Tx 2. 3.1 sinh e 3.2 %3D (Simiplify = Sech Cuox) answer fully your

A: Given

Q: sin 2t sin 5t 20 s4 + 58s2 + 441 O Option 3 None of the choices 1 10 s2 + 32 s2 + 72 s4 – 58s2 + 441

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Q: sin 3y limy0 5y 05 O 3/5 00 03

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Q: sinh (1+Inx)= Select one: ex-1 2xe O Zero e Inx 2 O None e?x² +1 2xe x² +1 O 1+ 2x

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Q: L = {cos² (3t)} L = {e-#£} 1 s2+72 (s+3)³ 1. 2s 2 - 2s2+72 (s+3) 1 2 2s s2+72 (s+3)² 1 + 2s 2s2+72 2…

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Q: Find L{(t – 1) (2 – 5 sin 3t)} . 2 2 15 15 + 83 s2 (s2 +9) 8(s2 +9) 2 15 30s s2+9 (s²+9)? 15 15 2 s3…

A:

Q: I-7 s² – 12 is 1 cosh2/3 t 2/3 а. 능 sinhv3 t V3 b. c. cosh2/3 t 1 sinh2/3 t 2/3 d.

A:

Q: 5s s + 4 s2 + 16 A. f(t) = 3e-4t - 5 cos 4t C. f(t) = 3e-4t – 5 sin 4a B. f(t) = 3e4t - 5 cos 4t D.…

A: Given F(s) = 3s + 4 - 5ss2 + 16

Q: sinh (Inx + Iny) = Select one: O None x²y² +1 2ху O 2xy O zero x²y² – 1 2хy x²– y? 2хy

A: To find: The value of sinhlnx+lny. Formula used: Logarithmic rule: ln a+ln b=ln ab Hyperbolic…

Q: 1 s³(5- 2)(5 + 2)' Select one: a. sinh2t O . ?e cosh2t C. t?sinh2t d. ?cosh2t е. t² e sinh2t

A:

Q: What is L S-7 (s+2)* - 49 A. e cosh3t + –e" e sinh 3t 3. 8. B. e cos 3t +e sin3t 31 С. -2/ cos 4t…

A:

Q: ( S L-1 e2s ( (s-6)²+25) u (t – 2) e6 (cos 5t + - sin 5t) O eor (cos 5t – sin 5t) и (1 — 2) е-6г…

A:

Q: 25 11 11 G(s) = Answer: 플-4t +t2-플e-2tcost -e-2t sint s3 (s2 +4s+5) 5 5

A: Use partial fraction to write G(s) in more simpler form.…

Q: 2a S (-1)*-1 NT sin x exp[-(nx/a)²t1] T(x,t) = a

A: The given equation is a heat(diffusion) equation.

Q: s-4 s+1 2. L(sin 2x + e2x+3) = . s²+4 s-2 Hint: e²x+3 = (e2x)(e³) -7s*+2s²+24 3. L(x* + x² – 7)

A: L{ eat}  = 1s-a    ,  L{sinat} = as2 + a2,     L{xn} = n!sn+11. L( e4x + e-x + x2  ) =L {e4x} + L{…

Q: Find L{(t – 1) (2 – 5 sin 3t)}. 2 15 15 + s(s² +9) s2 (s² +9) 5s 30s s2 +9 (82–9)² 2 15 15 s2 (s²…

A:

Q: Evaluate L{e (cosht – sinh nt)} 3r S+3 A. (s+3)*-n² (s+3)-a² S-3 B. (s -3)- (s-3) 2. s+3 C. (s+3) +*…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.