For a real number λ, consider the improper integrals
\(I_\lambda=\int_0^1 \frac{d x}{(1-x)^\lambda}\), \(K_\lambda=\int_1^{\infty} \frac{d x}{x^\lambda}\)
Which of the following statements are true?
1
There exists λ such that Iλ converges, but Kλ does not converge.
2
There exists λ such that Kλ converges, but Iλ does not converge.
3
There exists λ such that Iλ, Kλ both converge.
4
There exists λ such that neither Iλ, nor Kλ converges.