Theory questions

One of the problems on part C the exam will be a theoretical one. You might be asked to write down or use a definition, to formulate and prove a theorem or something like that. You might also be asked to give or analyse specific examples. The following might be part of such a problem on the exam:

* Definition of limit (ch. 1.5, definition 8 and definition 10)
* Definition of continuity (ch. 1.4, definition 4)
* Definition of the derivative (ch. 2.2, definition 4)
* Differentiable functions are continuous (ch. 2.3, theorem 1 and its proof)
* Product rule and quotient rule (ch. 2.3, theorems 3 and 5 and their proofs)
* The chain rule (ch. 2.4, theorem 6 and its proof)
* The mean value theorem and its consequences (ch. 2.8, theorems 11, 12, 13, 14 and 15 and proofs)
* Existence och localisation of extreme values (ch. 4.4, theorem 5 (without proof) and theorem 6 (with proof)
* Definition of linearization (ch. 4.9, definition 8)
* Taylor's formula (ch 4.10, theorem 12 without proof)
* The mean value theorem for integrals (ch. 5.4, theorem 4 with proof)
* The fundamental theorem of calculus (ch. 5.5, theorem 5 with proof)
* Substitution in integrals (ch. 5.6, theorem 6 with proof)
* Integration by parts (ch. 6.1, the formula on the bottom of page 332 and its derivation)
* Convergence of a sequence of numbers (ch. 9.1, definition 2)
* Convergence of a series (ch. 9.2, definition 3)
* Integral criterion for series (ch. 9.3, theorem 8)
* Comparison test for series (ch. 9.3, theorem 9)
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