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 (s-In 3) 16 (s-In 3)2 2 (s-In 4)3 9 (s-ln 4)2 e-4s + (s-3)3 8 (s-3)2 In 3 e-* ( 3 + ) 8. In 4 e-»(금 + 음) 6. s2

Q: 1 4 √x 5 18 dx =

A:

Q: 3. (2 + ln x)³ √ (2+1) X A. (2 + ln x) 4 +C -dx C. (2 + Inx)³ + C 4 {1tinx? Syn (2+1mx) +C 20 B. (2…

A: We can solve the integral using substitution method. Here we substitute 2+lnx by z and then apply…

Q: 2/3 = z/15

A:

Q: Q6.31 Look at the directional fields of phase planes below. Draw a line to match each phase plane…

A: A. Here for the given system ,eigenvalues of  are  ,complex with only imaginary part.Hence…

Q: Differentiate show human working please

A: Step 1:Step 2: Step 3: Step 4:

Q: 47. 27 fx-VI+x-4 dx × 7.60306

A: To show 2π∫13x-11+x-4dx≈7.60306

Q: 13: = 1 = dx 5sinx – 3cosx−2

A:

Q: Solve ry + (2r* – 1)y = 4x*e %3D

A: Solving the first order differential equation

Q: 2. (10 points) Evaluate 3x² (x3+5)² dx (using substitution)

A: Step 1:Step 2:

Q: sand is poured into a bucket for 30 seconds. after t seconds, the weight in sand is given by S(t) =…

A: sand is poured into a bucket for 30 seconds. after t seconds, the weight in sand is given by…

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.