1. Take 0.5 as a first approximation for <!--[if gte mso 9]><xml> <u1:WordDocument> <u1:View>Normal</u1:View> <u1:Zoom>0</u1:Zoom> <u1:TrackMoves/> <u1:TrackFormatting/> <u1:PunctuationKerning/> <u1:ValidateAgainstSchemas/> <u1:SaveIfXMLInvalid>false</u1:SaveIfXMLInvalid>...
1. Use mathematical induction to prove that for all integers n≥3
(1-2/3)(1-2/4)(1-2/5)...(1-2/n) = 2/n(n-1)
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1.The line AT is the tangent to the circle at A, and BT is a secant meeting at B and C.<o></o>
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(i)Write 8 cos x+ 6sinx in the form Acos(x -α), where A > 0 and 0 ≤ α ≤ π/2<o></o>
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(ii) Hence, or otherwise, solve the equation 8cosx + 6sinx = 5 for 0 ≤ x ≤ 2π<o></o>
Give...
1.i) Show that f(x)=e^x-3x^2 has a root between x=3.7 and x= 3.8
ii) Starting with x=3.8, use one application of Newtons method to find a better approximation for this root.
2.The function f(x)=sinx-2x/3 has a zero near x=1.5. Taking x=1.5 as a first approximation, use one application of...
I got a few past hsc questions which i have been doing, but i don't know if i've been doing them correctly as i don't have the answers.
1. Use the principle of mathematical induction to show that
2x1!+5x2!+10x3!+…+(n²+1)n!=n(n+1)!
For all integers positive n.
2.Use Mathematical...
1. The variable point ( 3t, 2t 2 ) lies on a parabola. Find the Cartesian equation for this parabola.
2.A curve has parametric equations x = t/2 , y = 3t² . Find the Cartesian equation for this curve.