Respuesta :
Answer:
sequence of five intervals
(1) 3³ < [tex]3^{\sqrt{10} }[/tex] < [tex]3^{4}[/tex]
(2) [tex]3^{3.1}[/tex] < [tex]3^{\sqrt{10} }[/tex] < [tex]3^{3.2}[/tex]
(3) [tex]3^{3.16}[/tex] < [tex]3^{\sqrt{10} }[/tex] < [tex]3^{3.17}[/tex]
(4) [tex]3^{3.162}[/tex] < [tex]3^{\sqrt{10} }[/tex] < [tex]3^{3.163}[/tex]
(5) [tex]3^{3.1622}[/tex] < [tex]3^{\sqrt{10} }[/tex] < [tex]3^{3.1623}[/tex]
Step-by-step explanation:
as per question given data
√10 ≈ 3.162 277 7
to find out
sequence of five intervals
solution
as we have given that √10 value that is here
√10 ≈ 3.162 277 7 ........................1
so
when we find [tex]3^{\sqrt{10} }[/tex] ................2
put here √10 value in equation number 2
we get [tex]3^{\sqrt{10} }[/tex] that is 32.27
so
sequence of five intervals
(1) 3³ < [tex]3^{\sqrt{10} }[/tex] < [tex]3^{4}[/tex]
(2) [tex]3^{3.1}[/tex] < [tex]3^{\sqrt{10} }[/tex] < [tex]3^{3.2}[/tex]
(3) [tex]3^{3.16}[/tex] < [tex]3^{\sqrt{10} }[/tex] < [tex]3^{3.17}[/tex]
(4) [tex]3^{3.162}[/tex] < [tex]3^{\sqrt{10} }[/tex] < [tex]3^{3.163}[/tex]
(5) [tex]3^{3.1622}[/tex] < [tex]3^{\sqrt{10} }[/tex] < [tex]3^{3.1623}[/tex]
