Q1: By employing convolution theorem, evaluate the following: s (4) L-¹ +as +bJia #b (5) I-¹ 1 (1) Z-¹ (s +1)(s +1) S (2) (1) [¹ (s+1) (s? - 1 (s' +a?) (3) 11 (6) L-¹ s?(s+1) 4s + 5 (S-1)² (s+2)

Q: Please prove 2(b)(iv)>(v)

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Q: Show that P(n, 1) + P(n, 2) = (22) – 2 (2), for integers n ≥ 2.

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Q: - 9x - 24 (x + 4)(x + 1) Evaluate ·S -dx + C

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Q: If the percent decrease is 25%, what is the common ratio?

A: Common Ratio The common ratio is defined as the amount between each number in a geometric sequence.…

Q: If y = 3, then dy de 3x+2" |3|

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Q: 16 If X-B (4, p) and P (X=0)=- then P (X=4) 81

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Q: If C(s)=16-2s2 then find a) C(3) b)C(-2) c)C(-1)

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Q: ´5s²–15s-11) -(s+1)(s–2)³. 34-2s 2. i) Find ii) Evaluate (15(s-5)(s+3).

A: The solution is given as

Q: 8 105 = 8 8 8+102 +. + %3D (1+r)' (1+r)² (1+r)³ ' (1+r)*

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Q: S(10) for √3 - 3 + 3√3+...

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Q: How does SN (1-r) = 1-√²+1 What are the operational rules of subscripts?

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Q: Show that * y = (y² – r*)(2² – x*)(2² – y³)

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Q: Suppose SCR is a set of numbers. (a) Define inf(S) and sup(S). (b) Show that inf(S) = - sup(-S). (c)…

A: Set: A well-defined collection of objects or numbers is called a set. We can write a set in two…

Q: Q4. Simplify the following expression: 3-5 x 39 Click on image to enlarge if needed 12 81 243 324

A: To evaluate :- 3-5 * 39

Q: Evaluate L{(t²+ 4)e³t} 2(2s² – 12s + 19) а) 2(2s² - b) 12s + 19) (s + 3)2 (s – 3)2 (2s2 – 12s + 19)…

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Q: For u(x) = 4x2 - x + 5 and v(x) = 2x + 4, which of the following is correct? a) (u – v)(2) = 11 b)…

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Q: 13D 43. If a > 1 and b < 0, then 1-101 (A) (B) 1 9 (a) (D) b(a+1) (E)

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