DP Mathematics HL Questionbank
The integral as a limit of a sum; lower and upper Riemann sums.
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- 18M.3ca.hl.TZ0.3d: Find an upper bound for \(\sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}} \).
- 18M.3ca.hl.TZ0.3c: Hence write down a lower bound for \(\sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}} \).
- 18M.3ca.hl.TZ0.3b: Illustrate graphically the...
- 18M.3ca.hl.TZ0.3a: Find the value of \(\int\limits_4^\infty {\frac{1}{{{x^3}}}{\text{d}}x} \).
- 12N.3ca.hl.TZ0.3c: Let \(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^2}}}} = L\) . The diagram below shows the graph...
- 08M.3ca.hl.TZ1.4: (a) Using the diagram, show that...
- 13M.3ca.hl.TZ0.5b: An improved upper bound can be found by considering Figure 2 which again shows part of the graph...
- 13M.3ca.hl.TZ0.5a: Figure 1 shows part of the graph of \(y = \frac{1}{x}\) together with line segments parallel to...
- 11N.3ca.hl.TZ0.4b: (i) Show, by means of a diagram, that...
- 15N.3ca.hl.TZ0.4b: Use the inequality in part (a) to find a lower and upper bound for \(\pi \).
