Lanza52
Oct10-07, 06:30 PM
Use the Comparisom Theorem to determine if
f(x) = \int^{\infty}_{42} \frac{42+42^-x}{x}dx
is convergent or divergent.
I compared it to g(x)=\int^{\infty}_{42} \frac{1}{x}dx
\int^{\infty}_{42} \frac{1}{x}dx = Lim_{t->\infty}\int^{t}_{42} \frac{1}{x}dx
Take the antiderivative, and the limit as t approaches infinity of ln(t)-ln(42) is infinity.
So divergent.
Looking for check. Thanks =P
f(x) = \int^{\infty}_{42} \frac{42+42^-x}{x}dx
is convergent or divergent.
I compared it to g(x)=\int^{\infty}_{42} \frac{1}{x}dx
\int^{\infty}_{42} \frac{1}{x}dx = Lim_{t->\infty}\int^{t}_{42} \frac{1}{x}dx
Take the antiderivative, and the limit as t approaches infinity of ln(t)-ln(42) is infinity.
So divergent.
Looking for check. Thanks =P