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 –9) s(s2 –9) 30s 15 + g2 +9 (s2 +9)? | | |

Q: •2 1 -dx- J-3 (x + 7)(x² + 16)

A: Given integral is Apply partial fractions to break the denominator

Q: 512x 1-x -3 - =—1 find volue of Σ(x²)"=? n=1

A: Given that the equation 512x1-x-3=-1   .

Q: (3x²-1) 5x3-5x+13 - dx equals In 15x³5x + 13| + c In 15x³ - 5x + c 5 O 1 In 15x³ - 5x + 13| + c 5 In…

A:

Q: Find [(5x + 4y)dA where D = {(x, y) | a² + y² ≤ 4, x ≥ 0}

A:

Q: dx x (In² x – 6 ln x + 10)

A:

Q: Ex:. Find the fourth roots of Z=-di Say no 4 K = 0₁12₂3

A: given z=-8i To find the fourth root of the given complex number proceed as follows comparing the…

Q: 2 x = (y-1)² x = 3 y 1 X = 2√y 2 x

A: Step 1:Step 2: Step 3: Step 4: thanks

Q: attached

A:

Q: dy Calculate . You need not expand your answer. 3x -6 y = (x– 3 )(x – 1)(x – 3) О а. 3(х - 3)(х…

A: Given,

Q: Evaluate (4x – 6x +1) dx, where A is a constant and A > -2. -2 O 443 – 6A + 20 O A4 – 3A2 + A - 2 O…

A: To evaluate ∫-2A4x3-6x+1dx

Q: 2π (9ピ)1 dt (18も)+(18ピ)

A:

Q: In(x-1) 33 Differentiate with respect to x. 2x + 3

A:

Q: Which of the following is equal to | (x6 – 7x)*dx 1 A (x5 – 7)5 +C - 25 B (x6 – 7x)5 + C - 1 (a6 –…

A:

Q: f (x) = { ₂x² (²/²) ² 2=1 Coso f(z) dz= ? 23

A: We have to calculate

Q: x-1 6)/2=0²+5² x² - 4x + 5 (1) (k) / zeaz² +b dz dx (i) (2x² – 5) sin x da (1) √²×² = √16x² dx

A:

Q: Consider the polynomial p(z) = z + 4z + 8. Evaluate it at the following values: (a) z = (b) z 2i 3 –…

A: We need to put the given values at the place of z

Q: x- 1 lim Vx² +3 – 2

A: given limit

Q: Find L L e2a sin (3t – 3a) da 3 A) F(s) (s-2)(s² +9) -3 B) F(s) (s+2)(s2 -9) 3s C) F(s) (s-2)(s2 +9)…

A: We find Laplace transform of given function

Q: (2+1) 2x + 5 (2x + 5)(2x) - (x² − 1)2 (x²-1)² - X 4x² +10x-2x² +2 2 (x²-1)² Dx || 2x² + 10x + 2…

A:

Q: Find the rational roots of x* + 8x + 7x-40x- 60= 0. 02,6 О-6, -2 O-2, 6 О-6, 2

A: Given  x4+8x3+7x2-40x-60=0 let, f(x)=x4+8x3+7x2-40x-60 Given that there is at least one and possibly…

Q: (a) Show that for n> 1 we have F2 = FnFn+1 − FnFn-1. (b) Use part (a) to show that F² + F² + . + F²…

A: Fn denote the Fibonacci sequence, satisfies Fn+1=Fn+Fn-1.              n≥2 And         F1=0,…

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: (C (g+1)n-((q+1)²-1) (g+1)n-[(g+2)²+(5q+3)] n-(q+1) (₁-2-(79+6)) II 1 + [²_o (q+1)k-(q+1)t-q k=1 = ⠀…

A: Given: The Information that leads to the required proof.We need to show the equations marked in red…

Q: Which of the following is not true? C 4dx 4dx A So √X(X+6) = lim So c+∞ ¹0 √x(x+6) 5 dx dx B S = lim…

A:

Q: -Vx2+5 -x f(x): f'(0)? -x+2

A:

Q: If esc() + + k = cot 3-2√3 3 0-√3 1 √3 O- 3-6 3 4T 3 then the exact value of k is

A: csc(π3)+k=cot(4π3)we know   cscx=1sinxtanx=1cotx

Q: - 1/5 Find (4) (n) for the function t(n)=5n 7/5 + 6n .

A:

Q: Find d dx [(5x³ - 2x) ¹] 3 4(5x³ - 2x) ³ 4(5x³ - 2x)³ (5x³ - 2x) (15x² − 2) 4x³ (15x² − 2) 3 4(5x³ –…

A: The given problem is solved below in detail.

Q: Question 2 Find for dx (a) y=(5x³-3)(x²+4x-1) (b) y=√x(2x²-3) dy (a)=25x¹+80x³-15x² - 6x - 12 A dy…

A: Solution