Question

iv only pls

(iv) Explain why it follows from (iv) that IV 2T+1 I(x) = Σ 2n+1 7and (2n +1)28 Like at least one of Euler's proofs, it derives the latter first and then deduces the former from it We will work with the function sin 2θ 1 + x cos 2θ ( tan-1 where T and θ are two independent variables. Sometimes we will regard x as the variable and sometimes and we will try to keep this clear. When x is the variable, you should assume θ is constant, and conversely (i) Show that ^ tan1 i) If we define a function I(x) by sin 26 1 + cos 2θ sin 2θ 1 + 2x cos 2θ + T2 ()tan-1(_rsin 20 do 1 + x cos 2θ it follows from (i) that I'(x) 1 + 2x cos 2θ + 2.2 . Show that 1,(x) = 2x in for-1

Answer 1

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