4 (-1)*- k² k=2 3k II

Q: 18 9s 52-4s+4 s2-4s+4

A: Consider the given expression. 9ss2-4s+4-18s2-4s+4   The objective of the problem is to simplify the…

Q: b) (-1)"3n² 4n²–1 n=1

A: We will use root test.

Q: V2k2 - 8– x = 0 %3D Ifk>0 and x = 2 in the equation above, what is k?

A: 2k2 - 83  - x = 0 We need to calculate the value of k.

Q: -8s2-5s+9 Find L- (s+1)(s² – 3s+2)

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Q: 6. Σ. 4n² - 9 n=1

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Q: у' + ху 3 ху a. IF = y2 b. IF = y3 C. IF = y² d. IF = y %3D

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Q: 6. Let [√16-X² Find y(2√3) 16-x? 2 16

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Q: L{tcos (-4t)} 16-s2 (s²+16)² s2+16 (s2–16)? - 16+s2 (s2-16)* s2-16 (s2+16)*

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Q: z(z+2) (z-1)(z-3) -1) - 12/3¹u(-n- -n-1) 9 3> z> x(n) zu(n 312 Option 4

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Q: Evaluate.

A: Given: ∑k=14 2k-10 Substitute the value of k=1, we get  21-10=-8 Substitute the value of k=2, we get…

Q: 32. y" + 4y = 8(1 - T) - 81 - 27). y(0) = 1. y'(0) = 0 33. y" + 3y' + 2y = 2u(1 – 2). y(0) = 0.…

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Q: 133. -Σ 2" Sn+ -(x + 2)" n=0

A: Consider the series, Rewrite this as Now take the constant outside,

Q: 27. * Σ n(n - 1)anan-2. n=2 + n=0 and

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Q: 15. Find x so that m || n. (5x – 20)°

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Q: Σ(-1)사2(1+ k k-1

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Q: 12 +3t-4 and 3t2-3 9.) Suppose that x = 3x 10

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Q: 12 -I Vk + 1 k=1

A: To find the sum, first, we need to check the convergence of the series. Here we use the divergence…

Q: ΣΕ (2) k%3D1

A: Answer

Q: 5. Describe the end behavior of P(x)=-6x-102x0 +3,297 a) as x→0, y00 and as x -o, y -o Opposite end…

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Q: - (x-2)" 3. n=0 3n +1

A: We find radius of convergence by ratio test, then find interval of convergence.

Q: Find (1s/(s²+4)} by convolutions

A: Given inverse Laplace transform

Q: Зх —7%3D 8х + 23-

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Q: 11. (x-y)2+ 3z 12. 4х - 2у 6z for x = 9, y = -3 and z = 7

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Q: 38. 32 (-1)k k=0 (2k + 1)³

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Q: Solve for n. k (3-n) %3D

A: b=k(3-n)pbp=k(3-n)

Q: 1) What is the sum of 8y 1- 2y? and -3y2 + 2y + 7?

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Q: 4 Σ n2 +4n +3 - 9-n+24n+1

A: Separate the sum.

Q: 1 Σ 3 k=1 Z (4 + 2k)

A: The given function can be represented as, fx=14+2x32 As per the Cauchy's Integral test, the series…

Q: Find the derivative

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Q: b. (− 1)* k² k=1 √kº +1

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Q: Q3 Suppose that X ~ N(-8, 14). Find:

A: Consider X as a random variable that follows a normal distribution with mean (-8) and standard…

Q: 2s Use Convolution to find L-1[- (s²+4)2-

A: Given: L-12ss2+42

Q: Solve 9tan(20) – 3/3 = 0 exactly on 0 < 0 < 2n. л 7л 13л 19л 0 = 12' 12' 12' 12 5л 11л 17я 23л 12'…

A: Given that 9tan2θ-33=0  and  0≤θ&lt;2πSolution :9tan2θ=33tan2θ=339=33=13tan2θ=13…

Q: Find a21 of A-1 Find a22 of A-1

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Q: 5x + 1 If y 2x-1 - In 7' then y' will be II

A: y=5x+12x-1-ln(7) In this we have to find differentiation of y. We know, ddxuv=vddxu-uddxvv2

Q: 5. Find (). 24e-5s L-1 S s2 – 9 s2 + 8s + 17

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Q: 2(-1)"-1 n²+4 n – 1 | n=1 n²+ 3

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Q: 2s2-s+4 s(s²+4) =4 + Bs+C s²+4

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Q: 18x°z³ 53 sume that all variables represent positive real numbers.

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Q: 3 1 b- k +1 k=0

A: To find the sum of the given summation

Q: 4N2 13 ds NG4-s2

A: We need to evaluate the value of the given integral

Q: 6 - 22n-1 5n+1 n=1 =D1

A: Given: ∑n=1∞6×22n-15n+1 A ∑n=1∞fn series is convergent if, fn+1fn&lt;1 Check the convergence of the…

Q: 5. Between z=-1.98 and z = -0.03

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Q: X-2y+2 = 0 8. 2x +3y + 18 = 0 10+ 10 10 sb loonbe s 26 701 8- -10+

A: Solving equations and graphing

Q: 5s2 – 15s – 11 - - L- (s + 1)(s – 2)3

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Q: 3- + - + 10 1 1 4. V2 1 1 3 V4 V5 (-1)"-1 5) Σ 2n + 1 n=1 /-

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Q: (-5)" n2 n- 1

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Q: 6. Between z= -1.53 and z=0

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Q: 2. 4s+32 s²-16

A: