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

The
`e^(4)` to one decimal is 54.6

Explanation:

we need to calculate
`e^(4)` to one decimal.

Since,
`e^(x)=1+(1)/(x!)+(x^(2))/(2!)+(x^(3))/(3!)+......` ....(1)

To calculate
`e^(4)` , put x=4 in equation (1)

`e^(4)=1+(1)/(4!)+(4^(2))/(2!)+(4^(3))/(3!)+......`

`e^(4)=1+(1)/(24)+(16)/(2)+(64)/(6)+......`

simplify the above expression

`e^(4)=1+(1)/(24)+(16)/(2)+(64)/(6)+(256)/(24)+(1024)/(120)......`

calculate with the scientific calulator

< 0.1 =54.6

Hence,
`e^(4)` to one decimal is 54.6