DP Mathematics HL Questionbank
Mean value theorem.
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- 16M.3ca.hl.TZ0.1c: (i) Use the Lagrange form of the error term to find an upper bound for the absolute value of...
- 16M.3ca.hl.TZ0.1b: Hence, or otherwise, determine the exact value of...
- 16M.3ca.hl.TZ0.1a: By finding a suitable number of derivatives of \(f\), determine the Maclaurin series for \(f(x)\)...
- 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...
- 15M.3ca.hl.TZ0.5a: The mean value theorem states that if \(f\) is a continuous function on \([a,{\text{ }}b]\) and...
- 15M.3ca.hl.TZ0.5b: (i) The function \(f\) is continuous on \([a,{\text{ }}b]\), differentiable on...
