DP Mathematics HL Questionbank
Taylor polynomials; the Lagrange form of the error term.
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[N/A]Directly related questions
- 18M.3ca.hl.TZ0.4d: Use this series approximation for \(f\left( x \right)\) with \(x = \frac{1}{2}\) to find an...
- 18M.3ca.hl.TZ0.4c: Hence show that the Maclaurin series for \(f\left( x \right)\) up to and including the term...
- 18M.3ca.hl.TZ0.4b: By differentiating the above equation twice, show...
- 18M.3ca.hl.TZ0.4a: Show that \(f'\left( 0 \right) = 0\).
- 16M.3ca.hl.TZ0.3b: Hence show that \(\ln (1.2)\) lies between \(\frac{1}{m}\) and \(\frac{1}{n}\), where \(m\),...
- 16M.3ca.hl.TZ0.3a: Given that \(f(x) = \ln x\), use the mean value theorem to show that, for \(0 < a < b\),...
- 16N.3ca.hl.TZ0.4c: Hence show that, for \(h > 0\) \(1 - \cos (h) \leqslant \frac{{{h^2}}}{2}\).
- 16N.3ca.hl.TZ0.4b: (i) Find \(g(0)\). (ii) Find \(g(h)\). (iii) Apply the mean value theorem to the...
- 16N.3ca.hl.TZ0.4a: State the mean value theorem for a function that is continuous on the closed interval...
- 16N.3ca.hl.TZ0.2c: By applying the ratio test, find the radius of convergence for this Maclaurin series.
- 16N.3ca.hl.TZ0.2b: Deduce that, for \(n \geqslant 2\), the coefficient of \({x^n}\) in this series is...
- 16N.3ca.hl.TZ0.2a: By successive differentiation find the first four non-zero terms in the Maclaurin series for...
- 08M.3ca.hl.TZ1.5: (a) Write down the value of the constant term in the Maclaurin series for \(f(x)\) . (b) ...
- 13M.3ca.hl.TZ0.1a: Find the values of \({a_0},{\text{ }}{a_1},{\text{ }}{a_2}\) and \({a_3}\).
- 15N.3ca.hl.TZ0.2b: By further differentiation of the result in part (a) , find the Maclaurin expansion of \(f(x)\),...
