Let a (> 1) be an irrational number. Show that the kth convergent of the simple continued fraction of /a is the reciprocal of the (k-1)th convergent of the simple continued fraction of a.

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A: Concept: Probablity=Total favourable outcomestotal outcomes

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Q: Evaluate t=0.01, Given: 21' + 20I = 100sin(150t) Round-off to 3 decimal places.

A: Given differential equation is2I'+20I=100sin150tI is evaluated at t=0.01 as shown below.

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Q: 17. Let T: P,¬R³ be the evaluation transformation at the sequence of points -1,0, 1. Find a. T(x2)…

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Q: EXAMPLE 4.4 Given the following data: -1 0. 3 y%3Df(x) Approximate f(2) by using Newton's divided…

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A: We approximate f(2) by using Newton's divided difference interpolation.

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Q: Consider the following Gauss elimination: O 0 1 0 1 0 EA → 0 9 |1 0 0 6 1 -6 9 -2 1 0|A → 0 E,E A →…

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Q: Verify Green's Theorem by evaluating both integrals |y? dx + x2 dy = Ne dA ду for the given path. C:…

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Q: 3. Use the integral test to show whether the series converges or diverges 00 п a) E- 00 1 b) E: n=4…

A: Integral test:  Suppose f(x) be a continuous, positive and decreasing function on the interval [m,…