Question

Let F(x)=int_{0}^{x}e^(-3t^4) dt
Find the MacLaurin polynomial of degree 5 for F(x).
Use this polynomial to estimate the value of
int_{0}^{0.11}e^(-3x^4) dx

Answer 1

\[F(x)=\int\limits_{0}^{x}e^(-3t^4) dt\]

Answer 2

i put 1-3x^4+3x^8/2!-3x^12/3!+3x^16/4! and it is not correct

Answer 3

\[\int\limits_{0}^{0.11}e^(-3x^4) dx\]

Answer 4

First let \[ h(x) = e^{-3 x^4}
\]
The MacLaurin polynmoial of Degree 4 of h at zero is
\[1- 3 x^4\]
Now the Maclaurin polynomial of degree 5 is
\[ g(x)=\int_0^x (1-3 t^4) dt = x - \frac {3 x^5} 5
\]
and
\[ g[.11] = .10999\]

Answer 5

i put 0.10999 and it is not correct

Answer 6

Give 4 or 5 significant digits

Answer 7

they are correct!!thanks!!