By Gray A., Mathews G.B.

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**Extra resources for A treatise on Bessel functions and their applications to physics**

**Example text**

5. 6. Is 9 continuous at every point in its domain 7 Answer : Yes. 7. Consider the lunction f 01 Example 1. Is f continuous (a) at 07 (b) at -27 (c) at27 Give reasons justilying your answers. §9. Limits In everyday language the word limit has virtually the same meaning as bound. In calculus, however, it has a rather different meaning. The limit of a function, at a certain point, is (roughly speaking) wh at the function, at that point, is on the threshold of doing. * If c is the point in quest ion, then the limit of f at c is symbolized by Limitf(x), (9) or by Limf at c, and is found by investigating the action of f at points near c, while completely ignoring the value off at c.

3. 4. 5. 6. Is 9 continuous at every point in its domain 7 Answer : Yes. 7. Consider the lunction f 01 Example 1. Is f continuous (a) at 07 (b) at -27 (c) at27 Give reasons justilying your answers. §9. Limits In everyday language the word limit has virtually the same meaning as bound. In calculus, however, it has a rather different meaning. The limit of a function, at a certain point, is (roughly speaking) wh at the function, at that point, is on the threshold of doing. * If c is the point in quest ion, then the limit of f at c is symbolized by Limitf(x), (9) or by Limf at c, and is found by investigating the action of f at points near c, while completely ignoring the value off at c.

C) What is 1 + 2 + 3 + 4 + 5 + 6 + 7'1 (d) What is 1 + 2 + 3 + ... + l00? ) (e) What is the sum ofthe first n positive integers? 3. The following principle is self-evident: If the same amount is taken away from two figures having equal area, then the two modified figures have equal area. It is thought that Pythagoras might have employed this principle, as folIows: a b b b b The two large squares have equal area. Take away the four right triangles, use the principle above, and it becomes clear" that c2 = a 2 + b2 .