DP Mathematics HL Questionbank

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• 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 $f(x)$,...