Improper Integrals and the Comparison Theorem

[Lanza52]

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

 

[Gib Z]

Yes that is correct.