Determine the numerical value of the following expression without the use of a calculator: log10 (1000100) 100 + X 100 n=1 sin(πn) + 1 (−1)n ! · vuut 1000 Y m=1 1 cos(πm) 2
Continue the two sequences of numbers below and find an equation to each of the sequences: n 1 2 3 4 5 6 7 Equation an 2 5 9 14 20 27 bn 1 3 12 60 360 2520
Prove that 2n+1 > (n + 2) · sin(n) for all positive integers n.
"Question1\n\nGiven A= [\u25a0(2&2&1@1&3&1@1&2&2)] \n\n\n\n\n1.1 find the eigenvalues of A\n\n1.2. Determine an eigenvector for the eigenvalue = 5\n\n\n\nQuestion2\nA periodic function f(x) with period 2 \u03c0 is defined by :\n f(x)= [ (x+\u03c0)\/2 -\u03c0\u02c2 X\u02c2 0, (x-\u03c0)\/2 0\u02c2 X\u02c2 \u03c0]\n\nDetermine the Fourier series for the periodic function"
Consider 3 distinct points M1, M2, and M3 with respective affixes z1, z2, and z3. Show that (Triangle M1, M2, and M3 is equilateral) ↔ ( z12 + z22 +z32 - z1z2 - z2z3 - z1z3).
Express 2x/ x2-1 in partial fractions and hence find the general solution of the differential equation dy/dx = 2xy / x2 - 1 expressing y explicitly in terms of x.
Explain any two purposes of assessing in emergent mathematics