#19 1:29( SafariRealAnalysis-ISBN-fix...+ y)?O!E(r+ y). OPROPERTY 3. If m is a positive integer then E(mr) = (E(r))". In particular,E(m) = (E(1))".CALCULUS IN THe 17TH AND 18TH CENTURIES41Problem 17. Prove Property 3.PROPERTY 4. E(-x) = x = (E(2))-.Problem 18. Prove Property 4.PROPERTY 5. If n is an integer with n+ 0, then E() = VE(1) = (E(1))/"Problem 19. Prove Property 5.PROPERTY 6. Ifm and n are integers with n # 0, then E () = (E(1))/".Problem 20. Prove Property 6.Definition 2. Let E(1) be denoted by the number e. Using the series e =E(1) = Eo, we can approrimate e to any degree of accuracy. In particulare 2.71828.In light of Property 6, we see that for any rational number r, E(r) = e". Notonly does this give us the series representation e" = Eo r" for any rationalnumber r, but it gives us a way to define e for irrational values of r as well.That is, we can definee = E(r) =for any real number z.As an illustration, we now have ev =E (V2)". The expression ev2 ismeaningless if we try to interpret it as one irrational number raised to another.What does it mean to raise anything to the v2 power? However the seriesEn (V2)" does seem to have meaning and it can be used to extend theexponential function to irrational exponents. In fact, defining the exponentialfunction via thie eorine anewore the oneetion un raiend on nase DT What doesNextDashboardCalendarTo DoNotificationsInbox因

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#19 1:29( SafariRealAnalysis-ISBN-fix...+ y)?O!E(r+ y). OPROPERTY 3. If m is a positive integer then E(mr) = (E(r))&#34;. In particular,E(m) = (E(1))&#34;.CALCULUS IN THe 17TH AND 18TH CENTURIES41Problem 17. Prove Property 3.PROPERTY 4. E(-x) = x = (E(2))-.Problem 18. Prove Property 4.PROPERTY 5. If n is an integer with n+ 0, then E() = VE(1) = (E(1))/&#34;Problem 19. Prove Property 5.PROPERTY 6. Ifm and n are integers with n # 0, then E () = (E(1))/&#34;.Problem 20. Prove Property 6.Definition 2. Let E(1) be denoted by the number e. Using the series e =E(1) = Eo, we can approrimate e to any degree of accuracy. In particulare 2.71828.In light of Property 6, we see that for any rational number r, E(r) = e&#34;. Notonly does this give us the series representation e&#34; = Eo r&#34; for any rationalnumber r, but it gives us a way to define e for irrational values of r as well.That is, we can definee = E(r) =for any real number z.As an illustration, we now have ev =E (V2)&#34;. The expression ev2 ismeaningless if we try to interpret it as one irrational number raised to another.What does it mean to raise anything to the v2 power? However the seriesEn (V2)&#34; does seem to have meaning and it can be used to extend theexponential function to irrational exponents. In fact, defining the exponentialfunction via thie eorine anewore the oneetion un raiend on nase DT What doesNextDashboardCalendarTo DoNotificationsInbox因

Accepted Answer

19. Given, if n is an integers with n≠0. Then show that                  E1n=E(1)n=E(1)1n