Consider the function f(x) = e0.3x. Use your calculator to answer the following questions. Determine the derivatives in the point a = 2. Give the values rounded to five decimals. f(0)(2) = f(1)(2) = f(2)(2) = f(3)(2) = f(4)(2) = Determine the third degree Taylor polynomial of f(x) = e0.3x about a = 2. Give the coefficients rounded to five decimals. T3(x) = Determine the value of the function in the point 5.2. Give the value rounded to five decimals.
Consider the function
f(x) = e0.3x.
Use your calculator to answer the following questions.
Determine the derivatives in the point a = 2. Give the values rounded to five decimals.
f(0)(2) =
f(1)(2) =
f(2)(2) =
f(3)(2) =
f(4)(2) =
Determine the third degree Taylor polynomial of f(x) = e0.3x about a = 2. Give the coefficients rounded to five decimals.
T3(x) =
Determine the value of the function in the point 5.2. Give the value rounded to five decimals.
f(5.2) =
Determine the value of the third degree Taylor polynomial of f(x) = e0.3x about a = 2 in the point 5.2. Give the value rounded to five decimals.
T3(5.2) =
Determine the absolute error between the function f(x) = e0.3x and the third degree Taylor polynomial of f(x) = e0.3x about a = 2 in the point 5.2. Give the value rounded to five decimals.
|f(5.2) - T3(5.2)| =
Determine the third degree remainder term of f(x) = e0.3x about a = 2. Give the coefficient rounded to five decimals.
R3(x) =( )e0.3c(x- )4
Determine the absolute maximum error between the function f(x) = e0.3x and the third degree Taylor polynomial of f(x) = e0.3x about a = 2 in the point 5.2. Give the value rounded to five decimals.
|R3(5.2)|max =
Determine the absolute maximum error between the function f(x) = e0.3x and the third degree Taylor polynomial of f(x) = e0.3x about a = 2 on the interval [0.3,6.7]. Give the value rounded to five decimals.
|R3(5.2)|max[0.3,6.7] =
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