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 $0 < a < b$,...
• 08M.3ca.hl.TZ1.5: (a)     Write down the value of the constant term in the Maclaurin series for $f(x)$ . (b)    ...
• 08M.3ca.hl.TZ2.4: (a)     Given that $y = \ln \cos x$ , show that the first two non-zero terms of the Maclaurin...
• 11M.3ca.hl.TZ0.1a: Find the first three terms of the Maclaurin series for $\ln (1 + {{\text{e}}^x})$ .
• 09M.3ca.hl.TZ0.2: The variables x and y are related by $\frac{{{\text{d}}y}}{{{\text{d}}x}} - y\tan x = \cos x$...
• 09N.3ca.hl.TZ0.2: The function f is defined by $f(x) = {{\text{e}}^{({{\text{e}}^x} - 1)}}$ . (a)     Assuming...
• SPNone.3ca.hl.TZ0.1b: (i)     Find the Maclaurin series for $f(x)$ up to and including the term in ${x^4}$ . (ii)...
• 10M.3ca.hl.TZ0.4: (a)     Using the Maclaurin series for ${(1 + x)^n}$, write down and simplify the Maclaurin...
• 10N.3ca.hl.TZ0.3: (a)     Using the Maclaurin series for the function ${{\text{e}}^x}$, write down the first four...
• 12N.3ca.hl.TZ0.4c: Using the Maclaurin series for $\ln (1 + x)$ , show that the Maclaurin series for...
• 14M.3ca.hl.TZ0.1b: Find the first three non-zero terms in the Maclaurin expansion of $f(x)$.
• 13N.3ca.hl.TZ0.4c: Hence determine the minimum number of terms of the expansion of $g(x)$ required to approximate...
• 14M.3ca.hl.TZ0.1a: Show that $f'(x) = g(x)$ and $g'(x) = f(x)$.
• 13N.3ca.hl.TZ0.4b: Use the Maclaurin series of $\sin x$ to show that...