Evaluate e^0.1 to four decimal places
what, no calculator?
1.1052
Now, if you're supposed to do it by hand,
1+.1/1!+.01/2!+.001/3!+.0001/4! = 1.1052
To evaluate e^0.1 to four decimal places, we can use the formula for the exponential function:
e^x = 1 + x/1! + x^2/2! + x^3/3! + ...
Here, x is the exponent, and '!' denotes the factorial. To evaluate e^0.1, we substitute x = 0.1 into the formula:
e^0.1 = 1 + (0.1)/1! + (0.1)^2/2! + (0.1)^3/3! + ...
Simplifying each term:
= 1 + 0.1 + (0.1)^2/2 + (0.1)^3/6 + ...
Next, we will continue adding terms until we achieve the desired level of accuracy, in this case, four decimal places. Let's calculate the first few terms:
= 1 + 0.1 + (0.1)^2/2 + (0.1)^3/6
= 1 + 0.1 + 0.005 + 0.0001667
≈ 1.1051667
Rounding this value to four decimal places, we get:
e^0.1 ≈ 1.1052
Therefore, e^0.1 to four decimal places is approximately 1.1052.