2. Use Huffman coding to encode these symbols with given frequen- cies: (a) a 0.35, b: 0.4, c: 0.2, d: 0.05. (b) a 0.15, b: 0.35, c: 0.23, d: 0.22, e: 0.04, f: 0.01.

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A:

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Q: Use the Laplace transform to solve the difference equation 3x(t) — 4x(t − 1) = 1, x(t)=0 for t < 0.

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Q: 8. [ csc5 xdx

A: Use the reduction formula.

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Q: Evaluate the following line integral.

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Q: [61] Diagonalize B = (by finding P and D) or explain why B isn't diagonalizable.

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Q: 19. Discuss the convergence of the series x²(log 2)9 + x³ (log 3)2 + x^(log 4) +

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Q: how do you do part d?

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Q: Find a basis for the space of 2 by 3 matrices whose nullspace contains (2, 1, 1 ).

A: To Find : The basis for the space of  2×3 matrices whose nullspace contains (2, 1, 1 ).

Q: Find Lad xdy + ydx, where C is the arc of the curve y = e for 0 ≤ x ≤ 2.

A: ∫Cxdy+ydx C: y=ex, 0≤x≤2