DP Mathematics HL Questionbank

• Syllabus

9.7

Sub sections and their related questions

The evaluation of limits of the form \(\mathop {\lim }\limits_{x \to a} \frac{{f\left( x \right)}}{{g\left( x \right)}}\) and \(\mathop {\lim }\limits_{x \to \infty } \frac{{f\left( x \right)}}{{g\left( x \right)}}\) .

• 12M.3ca.hl.TZ0.1: Use L’Hôpital’s Rule to find...
• 08M.3ca.hl.TZ2.1b: By using the series expansions for \({{\text{e}}^{{x^2}}}\) and cos x evaluate...
• 11M.3ca.hl.TZ0.1b: Hence, or otherwise, determine the value of...
• 09N.3ca.hl.TZ0.2: The function f is defined by \(f(x) = {{\text{e}}^{({{\text{e}}^x} - 1)}}\) . (a)     Assuming...
• SPNone.3ca.hl.TZ0.1c: Determine the value of \(\mathop {\lim }\limits_{x \to 0} \frac{{\ln (1 + \sin x) - x}}{{{x^2}}}\).
• 10M.3ca.hl.TZ0.4: (a)     Using the Maclaurin series for \({(1 + x)^n}\), write down and simplify the Maclaurin...
• 10N.3ca.hl.TZ0.1: Find \(\mathop {\lim }\limits_{x \to 0} \left( {\frac{{1 - \cos {x^6}}}{{{x^{12}}}}} \right)\).
• 13M.3ca.hl.TZ0.1b: Hence, or otherwise, find the value of...
• 11N.3ca.hl.TZ0.1: Find...
• 14M.3ca.hl.TZ0.1c: Hence find the value of \(\mathop {{\text{lim}}}\limits_{x \to 0} \frac{{1 - f(x)}}{{{x^2}}}\).
• 13N.3ca.hl.TZ0.4a: Using the result \(\mathop {{\text{lim}}}\limits_{t \to 0} \frac{{\sin t}}{t} = 1\), or...
• 16N.3ca.hl.TZ0.3a: Using l’Hôpital’s rule, find...

Using l’Hôpital’s rule or the Taylor series.

• 12M.3ca.hl.TZ0.1: Use L’Hôpital’s Rule to find...
• 08M.3ca.hl.TZ1.2: (a)     Using l’Hopital’s Rule, show that...
• 08M.3ca.hl.TZ2.1a: Find the value of...
• 08M.3ca.hl.TZ2.1b: By using the series expansions for \({{\text{e}}^{{x^2}}}\) and cos x evaluate...
• 08N.3ca.hl.TZ0.4: (a)     Show that the solution of the differential...
• 11M.3ca.hl.TZ0.1b: Hence, or otherwise, determine the value of...
• 09M.3ca.hl.TZ0.1a: Find \(\mathop {\lim }\limits_{x \to 0} \frac{{\tan x}}{{x + {x^2}}}\) ;
• 09M.3ca.hl.TZ0.1b: Find...
• 09N.3ca.hl.TZ0.2: The function f is defined by \(f(x) = {{\text{e}}^{({{\text{e}}^x} - 1)}}\) . (a)     Assuming...
• SPNone.3ca.hl.TZ0.1c: Determine the value of \(\mathop {\lim }\limits_{x \to 0} \frac{{\ln (1 + \sin x) - x}}{{{x^2}}}\).
• 10M.3ca.hl.TZ0.4: (a)     Using the Maclaurin series for \({(1 + x)^n}\), write down and simplify the Maclaurin...
• 10N.3ca.hl.TZ0.1: Find \(\mathop {\lim }\limits_{x \to 0} \left( {\frac{{1 - \cos {x^6}}}{{{x^{12}}}}} \right)\).
• 16N.3ca.hl.TZ0.3a: Using l’Hôpital’s rule, find...