DP Mathematics HL Questionbank

9.4
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[N/A]Directly related questions
- 18M.3ca.hl.TZ0.3d: Find an upper bound for ∞∑n=41n3.
- 18M.3ca.hl.TZ0.3c: Hence write down a lower bound for ∞∑n=41n3.
- 18M.3ca.hl.TZ0.3b: Illustrate graphically the...
- 18M.3ca.hl.TZ0.3a: Find the value of ∞∫41x3dx.
- 16M.3ca.hl.TZ0.2c: Hence obtain an expression for the derivative of...
- 16M.3ca.hl.TZ0.2b: By differentiating f(x2), obtain an expression for the derivative of...
- 16M.3ca.hl.TZ0.2a: Write down f′(x).
- 17M.3ca.hl.TZ0.5d: Explain why these two results prove that {Un} is a convergent sequence.
- 17M.3ca.hl.TZ0.5c.ii: Hence, given that n is a positive integer greater than one, show...
- 17M.3ca.hl.TZ0.5c.i: Hence, given that n is a positive integer greater than one, show that Un>0;
- 17M.3ca.hl.TZ0.5b.ii: Hence, given that n is a positive integer greater than one, show...
- 17M.3ca.hl.TZ0.5b.i: Hence, given that n is a positive integer greater than one, show...
- 17M.3ca.hl.TZ0.5a: By drawing a diagram and considering the area of a suitable region under the curve, show that for...
- 15N.3ca.hl.TZ0.4b: Use the inequality in part (a) to find a lower and upper bound for π.
- 12M.3ca.hl.TZ0.5a: Find the set of values of k for which the improper integral...
- 12N.3ca.hl.TZ0.3a: Prove that lim...
- 12N.3ca.hl.TZ0.3c: Let \sum\limits_{n = 1}^\infty {\frac{1}{{{n^2}}}} = L . The diagram below shows the graph...
- 12N.3ca.hl.TZ0.3e: You are given that L = \frac{{{\pi ^2}}}{6}. By taking k = 4 , use the upper bound and lower...
- 12N.3ca.hl.TZ0.3d: Hence show that...
- 08M.3ca.hl.TZ1.2: (a) Using l’Hopital’s Rule, show that...
- 08M.3ca.hl.TZ1.4: (a) Using the diagram, show that...
- 08M.3ca.hl.TZ2.2: Find the exact value of \int_0^\infty {\frac{{{\text{d}}x}}{{(x + 2)(2x + 1)}}} .
- 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...
- 14M.3ca.hl.TZ0.1d: Find the value of the improper integral...
Sub sections and their related questions
The integral as a limit of a sum; lower and upper Riemann sums.
- 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.TZ0.5a: Figure 1 shows part of the graph of y = \frac{1}{x} together with line segments parallel to...
- 13M.3ca.hl.TZ0.5b: An improved upper bound can be found by considering Figure 2 which again shows part of the graph...
- 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 .
- 18M.3ca.hl.TZ0.3a: Find the value of \int\limits_4^\infty {\frac{1}{{{x^3}}}{\text{d}}x} .
- 18M.3ca.hl.TZ0.3b: Illustrate graphically the...
- 18M.3ca.hl.TZ0.3c: Hence write down a lower bound for \sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}} .
- 18M.3ca.hl.TZ0.3d: Find an upper bound for \sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}} .
Fundamental theorem of calculus.
- 16M.3ca.hl.TZ0.2a: Write down f'(x).
- 16M.3ca.hl.TZ0.2b: By differentiating f({x^2}), obtain an expression for the derivative of...
- 16M.3ca.hl.TZ0.2c: Hence obtain an expression for the derivative of...
- 18M.3ca.hl.TZ0.3a: Find the value of \int\limits_4^\infty {\frac{1}{{{x^3}}}{\text{d}}x} .
- 18M.3ca.hl.TZ0.3b: Illustrate graphically the...
- 18M.3ca.hl.TZ0.3c: Hence write down a lower bound for \sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}} .
- 18M.3ca.hl.TZ0.3d: Find an upper bound for \sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}} .
Improper integrals of the type \int\limits_a^\infty {f\left( x \right){\text{d}}} x .
- 12M.3ca.hl.TZ0.5a: Find the set of values of k for which the improper integral...
- 12N.3ca.hl.TZ0.3a: Prove that \mathop {\lim }\limits_{H \to \infty } \int_a^H {\frac{1}{{{x^2}}}{\text{d}}x} ...
- 12N.3ca.hl.TZ0.3d: Hence show that...
- 12N.3ca.hl.TZ0.3e: You are given that L = \frac{{{\pi ^2}}}{6}. By taking k = 4 , use the upper bound and lower...
- 08M.3ca.hl.TZ1.2: (a) Using l’Hopital’s Rule, show that...
- 08M.3ca.hl.TZ2.2: Find the exact value of \int_0^\infty {\frac{{{\text{d}}x}}{{(x + 2)(2x + 1)}}} .
- 14M.3ca.hl.TZ0.1d: Find the value of the improper integral...
- 16M.3ca.hl.TZ0.2a: Write down f'(x).
- 16M.3ca.hl.TZ0.2b: By differentiating f({x^2}), obtain an expression for the derivative of...
- 16M.3ca.hl.TZ0.2c: Hence obtain an expression for the derivative of...
- 18M.3ca.hl.TZ0.3a: Find the value of \int\limits_4^\infty {\frac{1}{{{x^3}}}{\text{d}}x} .
- 18M.3ca.hl.TZ0.3b: Illustrate graphically the...
- 18M.3ca.hl.TZ0.3c: Hence write down a lower bound for \sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}} .
- 18M.3ca.hl.TZ0.3d: Find an upper bound for \sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}} .