Question

calculus 2: infinite limit http://puu.sh/2DqJZ.png

Answer 1

anyone??

Answer 2

you try integration by parts?

Answer 3

\[-\frac{ 1 }{ 3 }-13e ^{-\frac{ 4 }{ 3 }}\]

Answer 4

HOW??

Answer 5

integration by parts

Answer 6

\[\begin{array}{l}
\int\limits_4^n {f(x){e^{ - x/3}}dx} = \left[ {3f(x){e^{ - x/3}}} \right]_n^4 + 3\int\limits_4^n {f'(x){e^{ - x/3}}dx} \\
3\int\limits_4^n {f'(x){e^{ - x/3}}dx} = \int\limits_4^n {f(x){e^{ - x/3}}dx - } \left[ {3f(x){e^{ - x/3}}} \right]_n^4 \\
\end{array}\]

Answer 7

Evaluate \[\left[ {3f(x){e^{ - x/3}}} \right]_n^4\] using the first two conditions. Then take the limit on both sides as n goes to infinity.