O O Let F(s) = O est 5 e5t 5 est 5 + 6|5 t 5 O 6e5t 5 None of the others 1 s²-5 s 1 5 then £¹{F(s)} = ?

Q: Find x so that a || b. D. 5x (x + 12) 9-

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Q: r0 1-11 | Let B= 5 0 3 then det (2B)= %3D L1 3 0

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Q: (x + 5)/(x – 3) is NOT defined for x =   a. 3   b. 0   c. -3   d. -5

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Q: Vx + 3 Given f(x) = 4 then f-(x) will be %3D

A: The inverse function of a function f is a function that undoes the operation of f. The inverse of f…

Q: L(2 – 3t) ²= 4 12 18 .a O S s2 s3 4 9. .b O 4 6. 6 - S s2 S3 4 12 9. +. - s2 S3 +

A: Given that  L(2-3t)^2

Q: A (0,4) B (4.0) У 56 А K 3 2 3 415 6 X 0 (-3,0) D (0.-3)

A: Given query is to find  the point which lies in the solution region.

Q: In x

A: detailed solution with explanation is given below

Q: (x+ d

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Q: What is L (s-8) S-4 4r,2 A. e"r + 2e 4 B. et? +2e" 7 8t 2 4r C. e 32+2e 10 3r D. 2e" 3et0r 3r,3 E.…

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Q: 0.2(d - 6) = 0.3 d+ 5-3+0.1d %3D

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Q: 12. Solve 52+1>50. Round to the nearest ten-thousandth. A. (x|x2 0.7153) O B. (x|x 2 0) O C. (x|x 2…

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Q: Evaluate | x2 Q4. dx + 4x + 3

A: 4) To evaluate the integral

Q: Sx ³√x²+4 3 S

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Q: x³ + 27 dx . x+3 Evaluate x3 +9x + C 3 x3 3 +žx²+9x+C 3 x3 + x² – 9x + C 3 2 x3 3 x² + 9x+C 2 3

A: We know that, The sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power rule: ∫ax+bndx=ax+bn+1an+1+C And…

Q: b. 14-x²|dx

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

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: [4x 4xe³dx = + C

A: B=∫4xe3xdx∫xndx=xn+1n+1+c∫eaxdx=eaxa+c∫(a.b)dx=a∫bdx-∫(d dx(a)×∫bdx)dx

Q: 3x + 3x3 – 5x2 + x -1 dx x2 + x-2 Q4, Evaluate

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Q: dr I4 +3

A: Consider the given integral. I=∫x3x4+3dx

Q: Evaluate x2 dx

A: Use rules of integration

Q: dx 16. S 9x2-4 |3x+2 A. In +c B. In D. tn +C + C + C |3x+2 |3x+2| 3x-2

A: This is basic integration problem

Q: X+x 2. S x3-x²+x-1 -dx 4+5x2 3. S 4x+5x3 -dx

A: Given: ∫x2+xx3-x2+x-1dx

Q: (² 4 Calculate AT Let A = Select one: O a. O b. O C. O d. (63) 5 TOT -4 0 0 -2 -3 2B. 2 (9²) -5 -2 0…

A: The matrices are given by A = 0-24-3B = 21-11 To evaluate: The value of AT-2B.

Q: Show that [-3,0]| = |[-2, 7].

A: We say two sets have the same cardinality if there exists a bijection between the two sets.

Q: dy 7 +10y=0 is The CF of the d? dx O a. None of these O b. C.F. = (c +c,x)e* -3.x O c. CF=e2x + esx…

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Q: x=cos¬! 1 prove that sec" X= cos

A: Given sec-1x=cos-11x

Q: Q6 Frud +++

A: We have to find derivative

Q: S x² x²+49 -dx

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Q: 1 25. L-I s + 5s

A: Note : " As per our guidelines we will solve only first question . If you want any specific question…

Q: 유(In (e2x)) d dx 1 .a e2x 2х .b 1 .C 2 .d e2x O O

A: The solution is given below in the next step:

Q: -2 t Evaluate √5+² dx

A: Given integral is,To find : The solution of Integral.Integration rule used :where  is constant.

Q: x(In 7-2in 3)=-3ln 7-2in 3

A: The given expression xln 7-2 ln 3=-3 ln 7-2 ln 3. We have to find the value of x.