Answer:
The [tex]e^{4}[/tex] to one decimal is 54.6
Step-by-step explanation:
we need to calculate [tex]e^{4}[/tex] to one decimal.
Since, [tex]e^{x}=1+\frac{1}{x!}+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}+......[/tex] ....(1)
To calculate [tex]e^{4}[/tex] , put x=4 in equation (1)
[tex]e^{4}=1+\frac{1}{4!}+\frac{4^{2}}{2!}+\frac{4^{3}}{3!}+......[/tex]
[tex]e^{4}=1+\frac{1}{24}+\frac{16}{2}+\frac{64}{6}+......[/tex]
simplify the above expression
[tex]e^{4}=1+\frac{1}{24}+\frac{16}{2}+\frac{64}{6}+\frac{256}{24}+\frac{1024}{120}......[/tex]
calculate with the scientific calulator
< 0.1 =54.6
Hence, [tex]e^{4}[/tex] to one decimal is 54.6
