Existence and Properties of Non-Null Elements in E

Extract

[...] There is therefore a non-zero element in . For all the function is continuous and differentiable because and they are. Furthermore . sur so is decreasing on . so , so and finally is strictly decreasing. It is strictly monotone and continuous, so it is a bijection. when and when in a crescent compared between and . so it is a bijection of in . According to with . There is therefore a non-zero element in . We have shown that contained at least one non-null element for and for . [...]

[...] According to . The line is asymptote to the curve of en so so with . According to with . We have so the right is also asymptotic to the curve of TRANSLATED_TEXT . Search, for a real q positive or null, of non-null elements f of E such that = q f. For all the function is continuous and differentiable because and they are. Furthermore . car , so is growing. so , so so and finally is strictly increasing. [...]

[...] Let it be and elements of . If then so , so and finally . The application is therefore injective On a . All functions admits a primitive on , so we can say that for any function of , there is a function of primitive , tel que . The application is therefore surjective. is therefore bijective. Yes it is paired then so is a pair. Yes is odd then so it is uneven. Yes is limited to then as if so so it is therefore limited if it is also or . [...]