Question

Evaluate e^4 to one decimal place.

Answer 1

The answer is going to be the general form for e^x = 1 + x/(1!) + + x^2/(2!) + x^3/(3!) +.....,. till infinity so : e^4 = 1 + 4/1 + 16/ 2 + 64/6 + 256/24 + 1024/ 120 + 4096/720 + 16384/5040 +...till the fraction is<0.1 = 54.6

I hope this helps!

Answer 2

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