a Let A = d f h h i If det (A) = 10, what is the det (B), given B = kd ke kf|? %3D а C -k 10 10k -10k O -10

Q: 4. Find g[h(x)] if g(x) = x² and h(x) = x + 3. %3D O A. x2-- 3 B. x + 6x +9 O C. x + 3x? O D. z + a…

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Q: (a) 5(t + 3)dt (b) ſº25(t – 3)dt (c) In(t²)6(t – e)dt

A: Given:

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: Higher Order L.D.E (D3+D2-5D+3)2y=0

A: Higher Order L.D.E (D3+D2-5D+3)2y=0

Q: r.S a) Xn f(xla) · [la[x(1-x )]", a >o r lox)' r.S 6.) X, NCu, o?) o² is wmnknown 2 is unknown c.)…

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Q: 33]x = C],B = [] then, 4,l = f A = %3D 1. 16 2. 4 3. S 4. - 12

A:

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: d(a*) Suppose a E K, where a>0, a #1. What is dr A xa*-1 ха В a* © a*- In(a) D xa*-1. In(a) D ха

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Q: 10- The value of x³ J₁(x) dx is. 1-0 a) 8/(2) b) 8/₁(2) c) 8/2(2) d. 8/3 (2)

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Q: x²+1 If A = S* S dx, then A– x = %3D x²-4

A:

Q: If L{f(t)} = F(s) 3(s+3) and f(0.5) is s2+6s+8 e + 1 e2 (). given by K( : then find the value of K

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Q: S₁ A B If 2x²+x-2 (x+1)(x²+1) ² 1 -- 2 U NIG 5 —— D E) None + -S₂ -dx = A x + 1 + B (2x) + C x²+1…

A: Partial fraction decomposition

Q: Higher Order L.D.E (D-9)3y=0

A: The solution is given as

Q: If 2x²+x+1 S (x-1)(x+1)(x-2) A -2 B None 11 3 U D E - 3 11 3 A SA -dx = B + x-1 x+1 x-2 с -+ dx,…

A: Given, 2x2+x+1x-1x+1x-2

Q: 1+e of F(s) = 8(s2 s(s² + 9)

A:

Q: 4 Sadira made 4 different mixtures of red, blue, and white paint. The tables show the number of…

A: Quantity of the Blue paint and White paint for the respective mixtures are given in the table.

Q: -10 8. If S" f(x)dx = 4 and Siof(x)dx = 7, then f(x)dx = -3 %3D (a) 0 (b) –3 (c) 3 (d) 11 |

A: Given:-

Q: k k Ans. F(s)= 12) s(1+ea) 0 a 2а За 4а

A: Need to find laplace of given function

Q: 2.25 † Let I" -a" if x + a, f(x) = I-a if x = a, where n e N. Find the value of e that makes f E…

A:

Q: a. b. INGIN IN C. + S (S-1)² e35 + 5-1 e-3s S 5+1 d. None of the above L{2+ (t-3)et-3 U(t-3)] = +

A: Consider:  L2+t-3et-3 Ut-3=L2+Lt-3et-3 Ut-3 Now, L2=2L1=2×1s                      since L1=2s So,…

Q: 6x) 0<x<1 S(x)%=D , then p(x<1) is (a) 1 (b) 2 (c) 3 (d) 4 (c) None of these

A: It is an important part of statistics. It is widely used.

Q: 20 (i) E(13)* k=0 (ii) fºx'e-2= dx (iii) [ e-(z-13)²/8 dr

A:

Q: Evaluate : (a) L{e'u(t – 3)} (b) L{- 4e 3s (s-1)(s+3)

A:

Q: Ir X(s) (++2) (214)" find L[(2t)] Select one: O a. L[¤(2t)] (s+4) (s2+16) O b. L[r(2t)]| (8 | 4)…

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Q: 3) f(a) Va +1 & g(a) = & h(a) = Find (fogoh) %3D a+4

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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.

A:

Q: 2x²+x+1 S (x− 1)(x + 1)(x − 2) dx = ₁ 11 (A) 3 (B) None 11 C 3 (D) -SA+ 1 3 E -2 B + x+1 x-2 Q dx,…

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Q: ¹ Find the value of L-1 s²+6 [(s²+1)(s+4)]

A:

Q: A) a B) b ²¹dx = √( + g(x)) dx, then A + √² g(x) dx is equal to x³+x A. -1 B. −1+In(5/2) C. 1 D. -1…

A: Given; ∫x2-1x3+xdx=∫Ax+gxdx   As we know that; ∫1ax+bdx=1alnax+b+C

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: •a² +7 ra²+5 0.98Va-21 0.98v-21 dæ. dx 0, then a2+3 a2 +3

A: Use the property of integral and solve the inequality.

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: dx 4. S хV25-х2 5+Vx2-25 + C а. 5+Vx2-25 b. In + C c. --In 5+v25-x2 + C с. 5 d. None of the above

A:

Q: 2. m. n. e G)° dm dn 2 2 m² + m². e(m) + 2n²e)° т

A: Given differential equation, dmdn=2·m·n·enm2m2+m2·enm2+2n2enm2 To find the solution of differential…

Q: 11s+28 F(s) ise f(t)=L(F(s)]=? (s+2)².(s+5)

A:

Q: 5. S(e2r – e-2r)²dr S(e?r -2т е 2х 6. S dx 4-Зе2х

A:

Q: 1 d 1 d a a det 1 = 7 and det 2 = 11 e %3D e 1 f 3 f

A: Given: a1db1ec1f=7 and a1db2ec3f=11 To find: a) a3db3ec3f b) a3db5ec7f

Q: x²+x+1 so Ja 2x²+2+x²+x dx dx = [Aƒ (x) – B ln(g(x))] à + D fb +2 and if A=,B<0, then g(x) = .

A:

Q: S - 3 | c) F(s)= s2 + 4s + 3 s2 + 4s + 4 d) F(s) = (s – 1)(s – 2)(s + 4)'

A:

Q: 1 + a2x² 0 < x<1 e. w 3 Q1/ Let X be a r.v with p.d.f f(x) = }"1 and %3D Find 1. The value of a, and…

A: Given: fx=a1+a2x2,0≤x≤10,o.w.andEX=μ=35 The given function is probability density function if,…

Q: L(cosh 4t) = %3D s²+16 .b O s²-16 .C s2 – 4 I. .d O s2 - 8 SI

A: We will find Laplace transform of Cos hyperbolic function

Q: Evaluate the definite integral

A: Given,

Q: es L-1 (s- 1)(s +2)/ %3D O (1/3) e^t-(1/3)e^(-2t) O (1/3) e^2t-(1/3)e^(-2t) O [(1/3) e^(t-1)-(1/3)…

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

Q: S2 g(x)dx A. 1 f₂f(x) dx A. 2 Si[2 f(x) - g(x)]dx A. 4 B. O B. 10 B.20 C. −1 C.-2 C. -4 D. cannot be…

A:

Q: 10 a) F(s)=: s(s+2)(s+3)² s? b) F(s) =- s? +45+5

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: Question af If f(x, y) = xy² - x ln(y) find Ət if x(t, s) = s² - st³ and y(t, s) = e-st²

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Q: k+3 If fx+ k)dx=8, where k is constant, f(x+ J (x)dx=? then k-1

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Q: 5. y = xArctanx - In V1+x 6. y = In (e* + e*)

A: topic-second derivative of a function

Q: If w (x) = Ae^ikx for -L/2sxsL/2 ,normalize it, then A= 1 E 10 1 III O 2L .III O

A: given  ψx=Aeikx  for -L2≤x≤L2 normalize it then find the value of A first we find the complex…