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